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

Leading experts across smooth dynamics and ergodic theory present a broad research perspective and set an agenda for future work.

Danijela Damjanovic (Edited by), Boris Hasselblatt (Edited by), Andrey Gogolev (Edited by), Yakov Pesin (Edited by)

9781009278904, Cambridge University Press

Hardback, published 8 February 2024

446 pages
25.1 x 17.6 x 2.8 cm, 0.942 kg

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.

Editors note
1. Rigidity of topological entropy of boundary maps associated to Fuchsian groups
2. Open problems from 2020 vision for dynamics conference in Bedlewo
3. Flexibility of entropies for piecewise expanding unimodalm maps
4. Recent results and open questions on pseudo-rotations
5. SRB and equilibrium measures via dimension theory
6. Abelian Livshits theorems and geometric applications
7. A dynamical approach to validated numerics
8. Non-stationary normal forms for contracting extensions
9. Survey on entropy-type invariants of sub-exponential growth in dynamical systems
10. On the smooth realization problem and the AbC method
11. On some spectral problems in ergodic theory
12. Area preserving surface diffeomorphisms with polynomial decay of Correlation's are ubiquitous 13. Linear cocycles over hyperbolic systems.

Subject Areas: Calculus & mathematical analysis [PBK]