Yakov Pesin - Selected Publications#

1) Book: "Nonuniform Hyperbolicity: Dynamics of Systems with Nonzero Lyapunov Exponents" (with L. Barreira), Encyclopedia of Mathematics and Its Applications, 115, Cambridge University Press, 2007.

(This monograph represents further widespread progress of the non-uniform hyperbolicity (or Pesin) theory stimulated by such important examples like - among others - the completely novel translation flows, pseudo-Anosov maps, Hénon maps, etc. )

2) Book "Dimension Theory in Dynamical Systems: Contemporary Views and Applications", Chicago Lectures in Mathematics Series, University of Chicago Press, Chicago, 1997; Russian Translation, Moscow-Izevsk, 2002.

(This book describes the new area in dynamical systems theory that lies in the interface of geometric measure theory and dynamics and introduces new dimension-like characteristics of invariant sets and measures.)

3) "Partially hyperbolic dynamical systems" (with M. Brin), Mathematics USSR Izvestija, v. 8, N1 (1974) 177-218.

(The paper introduces the new concept of partial hyperbolicity and develops the fundamentals of the partial hyperbolicity theory.)

4) "Characteristic Lyapunov exponents and smooth ergodic theory", Russian Mathematical Surveys, v. 32, N4 (1977) 55-114.

(This epoch-making paper 1: introduces a new concept of non-uniform hyperbolicity and 2: develops the fundamentals of non-uniform hyperbolicity theory (commonly known as Pesin theory) including the 2/A: Stable Manifold theory, 2/B: Entropy formula (connecting Kolmogorov entropy with Lyapunov exponents), and a 2/C: Complete description of ergodic properties (up to the Bernoulli property) of volume preserving systems (with discrete and continuous time) with weak instability of trajectories. Applications include geodesic flows on compact Riemannian manifolds of non-positive curvature.)

5) "Gibbs measures for partially hyperbolic attractors" (with Ya. Sinai), Ergodic Theory and Dynamical Systems, v. 2, N3-4 (1983) 417-438. (The paper extends the famous Sinai-Ruelle-Bowen measures for classical hyperbolic attractors to partially hyperbolic ones and thus provides the basis for ergodic theory of partially hyperbolic attractors.)

6) "Ergodic properties and dimension-like characteristics of strange attractors that are close to hyperbolic", Proceedings of the International Congress of Mathematicians, Berkeley, USA (1987) 1195-1209.

7) "Equilibrium measures for coupled map lattices: existence, uniqueness, and finite-dimensional approximations" (with M. Jiang), Communications in Mathematical Physics, v. 193, N3 (1998) 675-711.

(This paper provides a complete description of equilibrium measures for the class of coupled map lattices -- an infinite chain of weakly interacting hyperbolic attractors - that are famous discrete models in mathematical physics , applied in physics, biology, etc. It reveals a persistent chaotic behavior in dynamical networks obtained by discretization of some famous evolution-type PDS.)

8)"Dimension and product structure of hyperbolic measures" (with L. Barreira and J. Schmeling), Annals of Mathematics., v. 149, N3 (1999) 755-783.

(The paper gives a complete solution of the Eckmann-Ruelle conjecture in dimension theory of smooth dynamical systems.)

9) "Every compact manifold carries a completely hyperbolic diffeomorphism" (with D. Dolgopyat), Ergodic Th. Dyn. Syst, v. 22 (2002) 1-27.

(The paper gives a solution of the long-standing problem in smooth ergodic theory on whether there are any topological obstructions for presence of a volume preserving smooth system with non-zero Lyapunov exponents.)

10) "Non-stationary non-uniform hyperbolicity: SRB measures for non-uniformly hyperbolic attractors" (with V. Climenhaga and D. Dolgopyat), Communications in Mathematical Physics, v. 346, N2 (2016) 553-602.

(The paper develops new mechanisms for constructing important Sinai-Ruelle-Bowen measures for systems with weak type of hyperbolic behavior.)

BY GOOGLE SCHOLAR:

Total number of citations 5393 (1567 since 2014), H-index 27 (18 since 2014), i10-index 45 (27 since 2014);
Total number of citations per year (last 5 years): 2014 - 250, 2015 - 260, 2016 - 250, 2017 - 400, 2018 - 380.

Paper 4) is most cited: It has 1595 citations, book 2) has 1104 citations and book 1) has 352 citations