# Modern Theory of Dynamical Systems: A Tribute to Dmitry Victorovich Anosov

Share this page *Edited by *
*Anatole Katok; Yakov Pesin; Federico Rodriguez Hertz*

It contains both original papers and surveys, written by some
distinguished experts in dynamics, which are related to important
themes of Anosov's work, as well as broadly interpreted further
crucial developments in the theory of dynamical systems that followed
Anosov's original work.

Also included is an article by A. Katok that presents Anosov's
scientific biography and a picture of the early development of
hyperbolicity theory in its various incarnations, complete and
partial, uniform and nonuniform.

# Table of Contents

## Modern Theory of Dynamical Systems: A Tribute to Dmitry Victorovich Anosov

- Cover Cover11
- Title page iii4
- Contents vii8
- Preface ix10
- Dmitry Viktorovich Anosov: His life and mathematics 112
- D. V. Anosov and our road to partial hyperbolicity 2334
- Escape from large holes in Anosov systems 2940
- A dynamical decomposition of the torus into pseudo-circles 3950
- On irreducibility and disjointness of Koopman and quasi-regular representations of weakly branch groups 5162
- Isolated elliptic fixed points for smooth Hamiltonians 6778
- Nonlocally maximal and premaximal hyperbolic sets 8394
- Rotation numbers for 𝑆² diffeomorphisms 101112
- Path connectedness and entropy density of the space of hyperbolic ergodic measures 111122
- Around Anosov-Weil Theory 123134
- Attractors and skew products 155166
- Thermodynamic formalism for some systems with countable Markov structures 177188
- 1. Motivation: Folklore Theorem in dimension 1 177188
- 2. Model under consideration. Geometric and hyperbolicity conditions 178189
- 3. Distortion conditions 180191
- 4. Additional hyperbolicity and distortion conditions and statement of the main theorem 181192
- 5. Hölder properties of log(𝐷^{𝑢}𝐹(𝑧)) 182193
- 6. Some sufficient conditions for exponential decay of correlations in countable shifts 189200
- 7. Proof of the exponential decay of correlations 191202
- References 192203

- Non-uniform measure rigidity for ℤ^{𝕜} actions of symplectic type 195206
- On a differentiable linearization theorem of Philip Hartman 209220
- Time change invariants for measure preserving flows 263274
- Spectral boundary value problems for Laplace–Beltrami operator: Moduli of continuity of eigenvalues under domain deformation 275286
- Measure-theoretical properties of center foliations 291302
- Back Cover Back Cover1334