Vladimir Arnold - Selected publications#

• 1. On the representability of functions of two variables in the form $\chi(\phi(x)+\psi(y))$. Uspehy Math. Nauk 1957, 12:2, 119-121.

• 2. On the functions of three variables. Doklady AN USSR, 1957, 114:4, 679-681.

• 3. On the representation of continuous functions of three variables by the superpositions of continuous functions of two variables. Matem. Sbornik, 1959, 48:1, 3-74 and 1962, 56:3, 392.

• 4. A criterion of the nomografibility on the rectangular Cartesian abacus. Uspehy Math. Nauk, 1961, 16:4, 133-135.

• 5. Small denominators. I: On the maps of a circle onto itself. Izvestija Ac. Sci. USSR, Ser. Math., 1961, 25:1, 21-86 and 1964, 28:2, 479-480.

• 6. On the stability of the equilibrium of a Hamiltonian system of ordinary differential equations in a generic elliptic case. Doklady AN USSR, 1961, 137:2, 255-257.

• 7. On the birth of a conditional-periodic motion from a family of periodic motions. Doklady, 1961, 138:1, 13-15.

• 8. Some remarks on the flows of linear elements and frames. Doklady, 1961, 138:2, 255-257.

• 9. Notes on the rotation numbers. Siberian Math. Jour., 1961, 2:6, 807-813.

• 10. On the behavior of adiabatic invariants under a slow periodic change of the Hamiltonian function. Doklady, 1962, 142:4, 758-761.

• 11. On small perturbations of automorphisms of tori (with Ya.G. Sinai), Doklady, 1962, 144:4, 695-698.

• 12. On the classical perturbation theory and stability theory of planetary systems. Doklady, 1962, 145:3, 487-490.

• 13. A proof of the A.N. Kolmogorov's theorem on the conservation of conditional-periodic motions in a small change of the Hamiltonian function. Uspehy Math. Nauk, 1963, 18:5, 13-40.

• 14. Small denominators and problems on the stability of motions in the classical and celestial mechanics. Uspehy Math. Nauk, 1963, 18:6, 91-192.

• 15. On one theorem of Liouville, concerning integrable problems of dynamics. Siberian Math. J., 1963, 4:2, 471-474.

• 16. Homogeneous distribution of points on a sphere and some ergodic properties of linear ordinary differential equations in the complex domain (with A.L. Krylov). Doklady, 1963, 148:1, 9-12.

• 17. On the nonstability of dynamical systems with many degrees of freedom. Doklady, 1964, 156:1, 9-12.

• 18. Conditions of the applicability and an estimate of the mistake of the averaging method for systems, which goes through the resonances during the evolution process. Doklady, 1965, 161:1, 9-12.

• 19. On the conditions of the nonlinear stability of flat stationary curvilinear flows of the ideal fluid. Doklady, 1965, 162:5, 975-978.

• 20. A Variational principle for three-dimensional stationary flows of the ideal fluid. Applied Math. and Mechan., 1965, 29:5, 846-851.

• 21. On the topology of three-dimensional stationary flows of the ideal fluid. Applied Math. and Mech., 1966, 30:1, 183-185.

• 22. Sur la courbure de Riemann des groupes de diffeomorphismes, C.R.Ac.Sci. Paris, 1965, v.260, 5668-5671.

• 23. Sur la topologie des ecoulements stationnaires des fluides parfaits, C.R.Ac.Sci. Paris, 1965, v.261, 17-20.

• 24. Sur une propriete topologique des applications globalement canoniques de la mecanique classique, C.R.Ac. Sci.Paris, 1965, 261, 3719-3722.

• 25. Sur la geometrie differentielle des groupes de Lie de dimension infinie et ses applications a l'hydrodynamique des fluides parfaits. Ann. Inst. Fourier, 1966, 16:1, 319-361.

• 26. Sur un principe variationel pour les ecoulements stationaires. J. de Mecanique, Paris, 1966, 5:1, 29-43.

• 27. Problemes ergodiques de la mecanique classique (with A. Avez). Gauthier-Villars, 1967, a book of 243 pages.

• 28. On one a priori estimate in the theory of the hydrodynamical stability. Izvestija VUZov, Ser.Mat., 1966, No.5, 3-5.

• 29. Stability problem and ergodic properties of classical dynamical systems. Proc. Intern. Congr. of Math. (Moscow, 1966); Trans. Congr. Intern. of Mathematicians (Moscow, 1966). Mir Publishers, 1968, 387-392.

• 30. On a characteristic class entering in the quantization conditions. Funct. Anal. and its Appl. (FAA), 1967, 1:1, 1-14.

• 31. A note on the Weierstrass preparation theorem. FAA, 1967, 1:3, 1-8.

• 32. Singularities of smooth mappings. Uspehy Math. Nauk, 1968, 23:1,3-44.

• 33. On braids of algebraic functions and cohomologies of swallowtails. Uspehy Math. Nauk, 1968, 23:4, 247-248.

• 34. A remark on the ramification of hyperelliptic integrals as functions of parameters. FAA 1968, 2:3, 1-3.

• 35. Notes on the singularities of finite codimension in the complex dynamical systems. FAA, 1969, 3:1, 1-6.

• 36. The cohomology ring of the group of colored braids. Mat.Zametki (Math. Notes), 1969, 5:2, 227-231.

• 37. On some topological invariants of algebraic functions, I. Trans. Moscow Math. Society, 1970, V.21, 27-46.

• 38. On one-dimensional cohomology of the Lie algebra of nondivergent vector fields and rotation numbers of dynamical systems. FAA, 1969, 3:4, 77-78.

• 39. Hamiltonial character of the Euler equations of dynamics of solids and of ideal fluid. Uspehy Math. Nauk, 1969, 24:6, 225-226.

• 40. On cohomology classes of algebraic functions, stable under Tschirnhausen transforms. FAA, 1970, 4:1, 84-85.

• 41. Topological invariants of algebraic functions, II. FAA, 1970, 4:2,1-9.

• 42. On local problems of Analysis. Vestnik Mosc. Univ., Ser. Math., 1970, No.2, 52-56.

• 43. Algebraic nonsolvability of the problem of Ljapunov stability and of the problem of the topological classification of singular points of analytic systems of differential equations. Uspehy Math. Nauk, 1970, 25:2, 265-266.

• 44. (The same title as for No.43) FAA, 1970, 4:3, 1-9.

• 45. On matrices depending on parameters. Rus. Math. Surv., 1971, 26:2, 101-114.

• 46. On the dispositions of ovals of real plane algebraic curves, involutions of four-dimensional smooth manifolds and arithmetics of integer quadratic forms. FAA 1971, 5:3, 1-9.

• 47. Ordinary differential equations. Moscow, Nauka, 1971, 1-240.

• 48. Notes on the behavior of flows of the three-dimensional ideal fluid under a small perturbation of the initial velocity field. Appl. Math. Mech. 1972, 36:2, 255-262.

• 49. A comment to "Sur un theoreme de la geometrie". In: Izbrannye trudy A.Puankare (H. Poincare, Selected Works), M., Nauka, 1972, vol.2, 987-989.

• 50. Integrals of rapidly oscillating functions and singularities of projections of Lagrange manifolds. FAA 1972, 6:3, 61-62.

• 51. Normal forms of functions near degenerate critical points, Weyl groups A, D, E and Lagrange singularities. FAA 1972, 6:4, 3-25.

• 52. Lectures on bifurcations and versal families. Rus. Math. Surv. 1972, 27:5, 119-182.

• 53. Modes and quasimodes. FAA 1972, 6:2, 12-20.

• 54. Classification of unimodal critical points of functions. FAA 1973, 7:3, 75-76.

• 55. Notes on the stationary phase method and Coxeter numbers. Uspehy Math. Nauk, 28:5, 1973, 17-44.

• 56. Normal forms of functions in a neighborhood of degenerate critical points. Rus. Math. Surv. 1974, 29:2, 11-49.

• 57. Topology of real algebraic curves (works of I.G.Petrovsky and their development). Uspehy Math. Nauk, 1974, 28:5, 260-262.

• 58. Critical points of functions and classification of caustics. Uspehy Math. Nauk, 1974, 29:2, 243-244.

• 59. Mathematical methods of classical mechanics. Moscow, Nauka, 1974, 432 p.

• 60. Asymptotical Hopf invariant and its applications. Trans. of All-Union School on differential equations. Erevan, 1974, 229-256 (Engl. translation: Selecta Math. Sov., 1986, 5:4, 327-346).

• 61. Critical point of smooth functions. Vancouver Intern. Congr. of Math., 1974, vol.1, 19-39.

• 62. Classification of bimodal critical points of functions. FAA 1975, 9:1, 49-50.

• 63. Critical points of smooth functions and their normal forms. Rus. Math. Surv., 1975, 30:5, 3-65.

• 64. Local normal forms of functions. Invent. Math. 1976, 35:1, 87-109.

• 65. A spectral sequence for the reduction of functions to normal forms. FAA 1975, 9:3, 81-82.

• 66. Spectral sequences for reduction of functions to normal forms. In: "Problems of mechanics and mathematical physics". Nauka, 1976, 7-20 (Engl. transl.: Selecta Math. Sov. 1:1, 1981, 3-18).

• 67. On the theory of envelopes. Uspehy Math. Nauk, 1976, 31:3, 248-249.

• 68. Some unsolved problems of the singularity theory. In: Trans. of the seminar of S.L.Sobolev. Novosubirsk, 1976, 5-15.

• 69. Bifurcation of invariant manifolds of differential equations and structure of the neighborhood of an elliptic curve on a complex surface. FAA, 1975, 10:4, 1-12.

• 70. Wave front evolution and equivariant Morse Lemma. Comm Pure and Appl. Math. 1976, 29:6, 557-582.

• 71. Loss of stability of autooscillations near resonances and versal deformations of equivariant vector fields. FAA 1977, 11:2, 1-10.

• 72. Index of a singular point of a vector field, Petrovsky-Oleinik inequalities and mixed Hodge structures. FAA 1978, 12:1, 1-14.

• 73. Critical points of functions on manifolds with boundary, simple Lie groups B, C, F and singularities of evolutes. Rus. Math. Surv. 1978, 33:5, 91-105.

• 74. Additional chapters of the theory of ordinary differential equations. Moscow, Nauka, 1978, 304 p.

• 75. Some problems of theory of differential equations. In: Non-solved problems of mechanics and mathematics. Moscow State Univ. Press 1977, 3-9.

• 76. On the contemporary development of I.G.Petrovsky's works on topology of real algebraic manifolds. Uspehy Math. Nauk, 1977, 32:3, 215-216.

• 77. Indices of singular points of 1-forms on a manifold with a boundary, convolution of invariants of groups generated by reflections, and singular projections of smooth surfaces. Uspehy Math. Nauk, 1979, 34:2, 3-36.

• 78. On some problems in singularity theory. In: Geometry and Analysis, Papers dedicated to the Memory of V.K. Patodi. Proc. Indian Ac. Sci., 99:1, 1981, 1-9.

• 79. Real algebraic geometry (with O.A. Oleinik). Vestnik (Bulletin) Moscow State Univ., Ser. 1, 1979, No.6, 7-17.

• 80. Stable oscillations whose potential energy is harmonic on the space and periodic on the time. Appl. Math. Mach. 1979, 43:2, 360-363.

• 81. Catastrophe theory. Priroda 1979, No.10, 54-63.

• 82. Statistics of integer convex polyhedra. FAA 1980, 14:2, 1-3.

• 83. Lagrange and Legendre cobordisms. FAA 1980, 14:3, 1-13 and 14:4, 8-17.

• 84. Catastrophe theory. Moscow, Znanie Publishers, 1981, 64 p.

• 85. Large scale structure of the Universe I. General properties. One and two-dimensional models (with Ya.B. Zeldovich and S.F. Shandarin). Preprint Inst. Appl. Math. No.100, 1981, 32 p. (Engl. transl.: Geophys. Astrophys. Fluid Dynamics 1982, V. 20, 111-130).

• 86. Large scale structure of the Universe (with Ya.B. Zeldovich and S.F. Shandarin). Rus. Math. Surv. 1981, 36:3, 244-245.

• 87. Sweeping of the caustic by the cusps of moving front. Uspehy Math. Nauk, 1981, 36:4, 233.

• 88. Magnetic field in a moving conducting liquid (with Ya.B. Zeldovich, A.A. Rusmaikin and D.D. Sokolov). Uspehy Math. Nauk, 1981, 36:5, 220-221.

• 89. Magnetic field in a stationary flow with expansions in a Riemannian space (with Ya. B. Zeldovich, A.A. Rusmaikin and D.D. Sokolov). J. of Exp. and Theor. Phys. 1981, 81:6, 2052-2058.

• 90. Lagrange manifolds with singularities, asymptotical rays and unfurled swallowtail. FAA 1981, 15:4, 1-14.

• 91. Asymptotical rays in symplectic and contact geometry. Uspehy Math. Nauk, 1982, 37:2, 182-183.

• 92. Singularities of differentiable maps I. Classification of critical points, caustics and wave fronts (with A.N. Varchenko and S.M. Gusein-Zade). Moscow, Nauka, 1982, 304 p.

• 93. Stationary magnetic field in a periodic flow (with Ya.B. Zeldovich, A.A. Rusmaikin, D.D. Sokolov). Doklady AN USSR 1982, 266:6, 1357-1358.

• 94. Singularities of Legendre varieties, of evolvents and of fronts at an obstacle. Ergodic Theory and Dyn. Systems, 1982, v.2, 301-309.

• 95. On the Newtonian attraction of a multitude of dust-like particles. Uspehy Math. Nauk, 1982, 37:4, 125.

• 96. Surgeries of singularities of potential flows in a collisionless media and metamorphoses of caustics in a three dimensional space. Trans. of the I.G. Petrovsky seminar, 1982, vol.8, 21-57.

• 97. Some notes on the antidynamo theorem. Vestnik (Bulletin) Mosk. State Univ., Ser.1, 1982, No.6, 50-57.

• 98. On the Newtonian potential oh hyperbolic layers. Memoirs of Tbilisi Univ. 1982, vol. 232-233, 23-28 (Engl. transl.: Selecta Math. Sov., 1985, 4:2, 103-106).

• 99. Increase of a magnetic field in a three-dimensional flow of a noncondensable fluid (with E.I. Korkina) Vestnik (Bull.) Mosc. State Univ., Ser.1, 1983, No.3, 43-46.

• 100. Evolution of a magnetic field under the action of translaton and difusion. Uspehy Math. Nauk, 1983, 38:2, 226-227.

• 101. Singularities of systems of rays. Uspehy Math. Nauk, 1983, 38:2, 77-147.

• 102. Notes on the perturbation theory for the problems of Matieu type. Uspehy Math. Nauk, 38:4, 1983, 189-203.

• 103. Singularities in the variational calculus. Contemp. Probl. of Math. 1983, v.22, 3-55 (Engl. transl.: J. Soviet Math.)

• 104. Singularities, bifurcations and catastrophes. Uspehy Phys. Nauk (Soviet Phys. Uspehy), 1983, 141:4, 569-590.

• 105. Catastrophe theory, extended 2-d edition. Mosc. State Univ. Press, 1983, 80 p.

• 106. Geometrical methods in the theory of ordinary differential equations. Springer, New York a.o., 1983, 334 p.

• 107. Magnetic analogues of the Newton's and Ivory's theorems. Uspehy Math. Nauk, 1983, 38:5, 145-146.

• 108. Some algebro-geometrical aspects of the Newton attraction theory. Progress in Math., Vol.36, Birkhauser, Basel, 1983, 1-3.

• 109. Some open problems in the theory of singularities. Proc. of Symposia in Pure Math., Vol.40 Part 1, 1983, p.57-69.

• 110. Singularities of functions, wave fronts, caustics and multidimensional integrals (with A.N. Varchenko, A.B. Givental and A.G. Khovansky). Mathematical Physics Reviews, Vol.4, 1984, 1-92.

• 111. Catastrophe theory. Springer, Berlin, 1984, 79 p.

• 112. Singularities of differentiable maps II. Monodromy and asymptotics of integrals (with A.N. Varchenko and S.M. Gusein-Zade). Moscow, Nauka, 1984, 336 p.

• 113. Vanishing inflexions. FAA 1984, 18:2, 51-52.

• 114. Some remarks on the elliptic coordinates. Notes of LOMI Scientific Seminars. 1984, v.133, 38-50.

• 115. Singularities in the variational calculus. Uspehy Math. Nauk, 1984, 39:5,256.

• 116. On the evolution of magnetic field under the action of translation and diffusion. In.: Some problems of contemporary analysis, Mosc. State Univ. Press, 1984, 8-21.

• 117. Reversible systems. In: Nonlinear and Turbulent Processes. Gordon and Breach, New York 1984, 1161-1174.

• 118. Exponential dispersion of trajectories and its hydrodynamical applications. In: N.E. Kotchin and Development of Mechanics. Moscow, Nauka, 1984, 185-193.

• 119. English translation of No.92. Birkhauser, Boston a.o. 1985, 1-385.

• 120. Singularities of Ray Systems. Proc. Intern. Congr. Math., August 16-24, 1983, Warszawa, Vol. 1, 27-49.

• 121. Ordinary differential equations. 3-d edition, revized and expanded. Moscow, Nauka, 1984, 1-272.

• 122. Ordinary differential equations (with Yu.S. Il'ashenko). Current Probl. Math. VINITI, Fundamental Directions, Vol.1. Moscow, VINITI, 1985, 7-149 (Engl. transl. in: Springer, Encycl. of Math. Sciences, Vol.1)

• 123. Period maps and Poisson structures. Uspehy Math. Nauk, 1985, 40:5, 236.

• 124. Sturm theorems and symplectic geometry. FAA, 19:4, 1985, 1-10.

• 125. Superpositions. In: A.N.Kolmogorov, Selected Works, Mechanics and Mathematics. Moscow, Nauka, 1985, 444-451.

• 126. Classical mechanics. In: A.N.Kolmogorov, Selected Works, Moscow, Nauka, 1985, 433-444.

• 127. Implicit differential equations, contact structures and relaxation oscillations. Uspehy Math. Nauk, 40:5 (1985), 188.

• 128. Mathematical aspects of classical and Celestial Mechanics (with V.V. Kozlov and A.I. Neistadt). Moscow, VINITI, 1985. (Engl. transl.: Springer, Encycl. of Math. Sciences, Vol.3).

• 129. Symplectic geometry (with A.B. Givental). Current Probl. in Math. VINITI, Fundam. Directions, Vol.4. Moscow, VINITI, 1985, 7-139. (Engl. transl. in: Springer, Encycl. Math. Sciences, Vol.4)

• 130. On some nonlinear problems. In: Crafoord prize in mathematics, 1982. Crafoord lectures, The Royal Swedish Ac. of Sci., 1986, 1-7.

• 131. Catastrophe Theory. Second revized and expanded edition. Springer, Berlin, 1986, 108 pages.

• 132. Hyperbolic polynomials and Vandermond maps. FAA 20:2, 1986, 52-53.

• 133. Singularities of boundaries of spaces of differential equations. Uspehy Math. Nauk, 41:4, 1986, 152-154.

• 134. First steps of symplectic topology. Rus. Math. Surv., 41:6, 1986, 3-18.

• 135. Catastrophe theory and new possibilities of the application of mathematics. In: Mathematization of the contemporary science. Moscow, 1986, 81-87.

• 136. Bifurcation theory (with V.C. Afraimovitch, Yu.S. Il'ashenko and L.P. Shil'nikov). Current probl. of Math. VINITI, Fund. Directions, Vol.5. Moscow, VINITI, 1986, 5-218. (Engl. transl. in: Springer, Berlin a.o., Encycl. of Math. Sciences, Vol. 5)

• 137. Catastrophe theory. The same issue as for No.136, 219-277.

• 138. Oscillations and bifurcations in reversible systems (with M.B. Sevrjuk). In: Nonlinear Phenomena in plasma physics and Hydrodynamics, ed.: R.Z. Sagdeev. Mir Publishers, 1986, 31-64.

• 139. French translation of No. 92 and No. 112. Moscow, Mir Publishers, 1986.

• 140. 300-th Anniversary of the mathematical natural philosophy and celestial mechanics. Priroda, 1987, No.8(864), 5-15.

• 141. Hungarian edition of No.46. Budapest, 1987.

• 142. Quasicrystalls, Penrose partitions, Markov partitions, stochastic web and singularity theory. Uspehy Math. Nauk, 42:4, 1987, 139.

• 143. Second Kepler's law and topology of Abelian integrals (according to I.Newton). Kvant, 1987, No.12, 17-21.

• 144. Convex hulls and encreasing of productivity of systems in the pulsatory load. Siberian Math. J., 28:4, 1987, 29-31.

• 145. Contact structure, relaxational oscillations and singular points of implicit differential equations. In: Geometry and singularity theory in nonlinear equations. Voronezh, 1987, 3-8.

• 146. Portuguese transl. of No.59. Mir Publishers, 1987

• 147. Topological proof of the trnscendence of Abelian integrals in the Newtons "Principia". Histor.-Math. Investigations, XXXI, Moscow, Nauka, 1989, 7-17.

• 148. Ramified covering CP2 ? S4 , hyperbolicity and projective topology. Siberian Math. J., 29:5, 1988, 36-47.

• 149. Notes on the Poisson structures on the plane and other powers of the volume forms. Trans. of the I.G.Petrovsky seminar, No.12, 1987, 37-46.

• 150. German transl. of No. 72. Birkhauser, Basel, 1987, 320 p.

• 151. Mathematics with a human face. Priroda 1988, No.3, 117-119.

• 152. On surfaces, defined by hyperbolic equations. Matem Zametki (Math. Notices) 1988, 44:1, 3-17.

• 153. Remarks on quasicrystallic symmetries. Physica D, nonlinear phenomena. 1988, 33:(1-3), 21-25.

• 154. On some problems in symplectic topology. In: Topology and Geometry. Rohlin Seminar. O.Ya.Viro (Ed.) Springer Lecture Notes Math., 1346 (1988), 1-5.

• 155. On the interior scattering of waves, defined by hyperbolic variational principles. J. of Geometry and Physics 1988. Vol.V, No.3, 305-315.

• 156. Bifurcations and singularities in mathematics and mechanics. In: Theoretical and Applied Mechanics XVII IUTAM, Congress, Grenoble, 1988. Elsevier, 1989, 1-25.

• 157. German transl. of No.59. VEB Deutscher Verlag der Wissenschaften DDR, 520, 1988.

• 158. Singularities I. Local and Global Theory (with V.A. Vassil'ev, V.V. Gorjunov and O.V. Ljashko). Moscow, VINITI, 1988, 1-256 (to be transl. by Springer as Vol.6 of Encycl. Math. Sciences).

• 159. Singularities II. Classification and Applications (with V.A. Vassil'ev, V.V. Gorjunov and O.V. Ljashko). Moscow, VINITI, 1989, 1-256 (to be transl. by Springer as Vol. 39 of Encycl. Math. Sci.).

• 160. Dynamics of intersections. In: Analysis, et cetera. Research papers Published in Honor of Jurgen Moser's 60-th Birthday. Eds. P.Rabinovitz, E. Zehnder. Acad. Press, San Diego, 1990, 77-84.

• 161. A-graded algebras with 3 generators. Comm. Pure Appl. Math., 42, 1989, 993-1000.

• 162. Engl. transl. of No.112. Birkhauser, Boston a.o., 492 p.

• 163. Some words on Andrei Nikolaevich Kolmogorov. Uspehy Math. Nauk, 43:6, 1988, 34.

• 164. A.N.Kolmogorov in the reminiscences of pupils. Kvant, 1988, No.11-12, 34.

• 165. A.N.Kolmogorov, obituary. Physics today. 42:10, 1989, 148-150.

• 166. Contact structure, relaxation oscillations and singular points of implicit differential equations, in: Springer Lecture Notes Math., 1334, 173-179; 1988.

• 167. Spaces of functions with mild singularities. FAA, 23:3, 1988, 1-10.

• 168. Teoria delle catastrofi. Bollati Boringhieri, Torino, 1990, 146 p.

• 169. Newton's principia read 300 Years later (with V.A. Vassil'ev). Notices of the Amer. Math. Soc., 1989, 36:9, 1148-1154 and 37:2 (1990), 144.

• 170. Some unsolved problems of theory of differential equations and mathematical physics. Uspehy Math. Nauk, 1989, 44:4, 191-192.

• 171. Contact geometry: the geometrical method of Gibbs thermodynamics. AMS, 1990.

• 172. Singularity theory and its applications. Lezioni Fermiane. Academia Nazionale Dei Lincei. Scuola Normale Superiore. Pisa, 1990.

• 173. Catastrophe theory. Nauka i zhish'n (Science and life) 1989 No.10, 12-19.

• 174. Contact geometry and wave propagation. Monographie No.34 Enseign. Math., 1989, 56 pages.

• 175. Ten problems. In: Singularity theory and its applications. Adv. in Soviet math. Vol. 1. AMS, 1990, 1-8.

• 176. One hundred problems. MFTI, Moscow, 1989.

• 177. Bernoulli-Euler updown numbers associated with function singularities, their combinatorics and arithmetics. Duke Math. J., 63:2, 1991, 537-555.

• 178. Dynamics of complexity of intersections. Boletim da Sociedade Brasiliera de Mathematica 21:1, 1990, 1-10.

• 179. Huygens and Barrow, Newton and Hooke, Birkhauser, Basel a.o., 1990, 118 p.

• 180. Mathematical trivium. Uspehy Math Nauk, 46:1, 1991, 225-232.

• 181. Catastrophe theory. 3-d edition, extended. Moscow, Nauka, 1990, 128 p.

• 182. 3-d edition of No.59, extended. Moscow, Nauka, 1988. 472 p.

• 183. Singularities of Caustics and Wave Fronts. Kluwer, 1990.

• 184. Topological and ergodic properties of a closed differential 1-form, Func. Anal. Appl. 25:2 (1991),1-12.

• 185. Meanders. Kvant, 1991, no. 3, pp. 11-14.

• 186. Majoration of Milnor numbers of intersections in holomorphic dynamical systems, preprint 652 Utrecht Univ., April 1991, 1-9 (Topological Methods in Modern Mathematics, Publish or Perish 1992).

• 187. Springer numbers and morsification spaces, prprint 658 Utrecht Univ., April 1991, pp. 1-18. (J. Alg. Geom. 1:2, 1992)

• 188. Calculus of snakes, Uspehi Math. Nauk., 47, v. 2, 1992.

• 189. Problems on singularities and dynamical systems, Progress in Sov. Math., Chapman and Hall, 1992.

• 190. Topological methods in hydrodynamics (with B.A. Khesin), Annual Reviews in Fluid Dynamics, 24, 1992.

• 191. Mathematical trivium - II. Uspehy Math Nauk, 48:1, 1993, 211-222.

• 192. Bounds for Milnor numbers of intersections in holomorphic dynamical systems. In: Topological methods in Modern Mathematics (Stony Brook, NY, 1991). - Houston, TX: Publish or Perish, 1993, 379--390.

• 193. Sur les proprietes topologiques des projections lagrangiennes en geometrie symplectique des caustiques. -- CEREMADE, Universite Paris-Dauphine. Cahiers de Mathematiques de la Decision, 9320, 14.06.93, 9 p.

• 194. On the topological properties of Legendrian projections in the contact geometry of wave fronts. Algebra and Analysis, 1994, 6(3), 1--16 (in Russian).

• 195. Topological Invariants of Plane Curves and Caustics. Dean Jacqueline B. Lewis Memorial Lectures, Rutgers University. -- Providence, RI: Amer. Math. Soc., 1994, VIII+60 p. (University Lecture Series, 5).

• 196. Topological classification of real trigonometric polynomials and cyclic serpents polyhedron. In: Arnold--Gelfand Mathematical Seminars. -- Boston: Birkhauser, 1996.

• 197. Toronto lectures, June 1997 Lecture 1: From Hilbert's Superposition Problem to Dynamical Systems. Lecture 2: Symplectization, Complexification and Mathematical Trinities. Lecture 3: Topological Problems in Wave Propagation Theory and Topological Economy Principle in Algebraic Geometry. (available at http://www.botik.ru/~duzhin/arnold/arn-papers.html).

• 198. On the problem of realization of a given Gaussian curvature function.