A Vision for Dynamics in the 21st Century: The Legacy of Anatole Katok

doi:10.1017/9781009278898

A large international conference celebrated the 50-year career of Anatole Katok and the body of research across smooth dynamics and ergodic theory that he touched. In this book many leading experts provide an account of the latest developments at the research frontier and together set an agenda for future work, including an explicit problem list. This includes elliptic, parabolic, and hyperbolic smooth dynamics, ergodic theory, smooth ergodic theory, and actions of higher-rank groups. The chapters are written in a readable style and give a broad view of each topic; they blend the most current results with the developments leading up to them, and give a perspective on future work. This book is ideal for graduate students, instructors and researchers across all research areas in dynamical systems and related subjects.

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Contents

Frontmatter
pp i-iv
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Contents
pp v-vi
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Editor’s Note
pp vii-vii
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List of Contributors
pp viii-x
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1 - Open Problems from 2020 Vision for Dynamics Conference in Będlewo
pp 1-18
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2 - Rigidity of Topological Entropy of Boundary Maps Associated to Fuchsian Groups
pp 19-47
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3 - Flexibility of Entropies for Piecewise Expanding Unimodal Maps
pp 48-66
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4 - Recent Results and Open Questions on Pseudo-Rotations
pp 67-93
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5 - SRB and Equilibrium Measures via Dimension Theory
pp 94-138
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6 - Abelian Livshits Theorems and Geometric Applications
pp 139-167
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7 - A Dynamical Approach to Validated Numerics
pp 168-206
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8 - Non-stationary Normal Forms for Contracting Extensions
pp 207-231
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9 - Survey on Entropy-Type Invariants of Subexponential Growth in Dynamical Systems
pp 232-289
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10 - On the Smooth Realization Problem and the AbC Method
pp 290-317
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11 - On Some Spectral Problems in Ergodic Theory
pp 318-336
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12 - Area-Preserving Surface Diffeomorphisms with Polynomial Decay of Correlations Are Ubiquitous
pp 337-383
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13 - Linear Cocycles over Hyperbolic Systems
pp 384-434
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A Vision for Dynamics in the 21st Century

The Legacy of Anatole Katok

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Contents

Frontmatter
pp i-iv

Contents
pp v-vi

Editor’s Note
pp vii-vii

List of Contributors
pp viii-x

1 - Open Problems from 2020 Vision for Dynamics Conference in Będlewo
pp 1-18

2 - Rigidity of Topological Entropy of Boundary Maps Associated to Fuchsian Groups
pp 19-47

3 - Flexibility of Entropies for Piecewise Expanding Unimodal Maps
pp 48-66

4 - Recent Results and Open Questions on Pseudo-Rotations
pp 67-93

5 - SRB and Equilibrium Measures via Dimension Theory
pp 94-138

6 - Abelian Livshits Theorems and Geometric Applications
pp 139-167

7 - A Dynamical Approach to Validated Numerics
pp 168-206

8 - Non-stationary Normal Forms for Contracting Extensions
pp 207-231

9 - Survey on Entropy-Type Invariants of Subexponential Growth in Dynamical Systems
pp 232-289

10 - On the Smooth Realization Problem and the AbC Method
pp 290-317

11 - On Some Spectral Problems in Ergodic Theory
pp 318-336

12 - Area-Preserving Surface Diffeomorphisms with Polynomial Decay of Correlations Are Ubiquitous
pp 337-383

13 - Linear Cocycles over Hyperbolic Systems
pp 384-434

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The Legacy of Anatole Katok

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