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A Vision for Dynamics in the 21st Century

A Vision for Dynamics in the 21st Century

A Vision for Dynamics in the 21st Century

The Legacy of Anatole Katok
Danijela Damjanovic, KTH Royal Institute of Technology, Stockholm
Boris Hasselblatt, Tufts University, Massachusetts
Andrey Gogolev, Ohio State University
Yakov Pesin, Pennsylvania State University
January 2024
This ISBN is for an eBook version which is distributed on our behalf by a third party.
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9781009278874
$170.00
USD
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Hardback

    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.

    • Written by a broad range of leading experts, providing a wide and specialized perspective on the discipline
    • Presents results from the current forefront of dynamical systems, setting an agenda for future research
    • Inspired by the Legacy of Professor Anatole Katok, presenting his pivotal research and celebrating his contribution to the field

    Product details

    January 2024
    Adobe eBook Reader
    9781009278874
    0 pages
    This ISBN is for an eBook version which is distributed on our behalf by a third party.

    Table of Contents

    • 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.
      Contributors
    • Adam Abrams, Svetlana Katok, Ilie Ugarcovici, Jairo Bochi, Danijela Damjanovic, Lluís Alesedà, Michal Misiurewicz, Rodrigo A. Pérez, Baney Bramham, Zhiyuan Zhang, Vaughn Climenhaga, Andrey Gogolev, Federico Rodriguez Hertz, Oliver Jenkinson, Mark Pollicott, Boris Kalinin, Adam Kanigowski, Anatole Katok, Daren Wei, Phillip Kunde, Mariusz Lemanczyk, Yakov Pesin, Samuel Senti, Farruh Shahidi, Victoria Sadovskaya

    • Editors
    • Danijela Damjanovic , KTH Royal Institute of Technology, Stockholm

      Danijela Damjanovic is an Associate Professor at the Royal Institute of Technology (KTH), Sweden. She received her PhD in mathematics from Pennsylvania State University, USA in 2004. Her research is in the area of dynamics of smooth group actions. She serves on the editorial board of Journal of Modern Dynamics.

    • Boris Hasselblatt , Tufts University, Massachusetts

      Boris Hasselblatt is a professor at Tufts University, USA. He received his PhD from California Institute of Technology in 1989. He is a co-author of several books in the field of smooth dynamical systems, notably Introduction to the Modern Theory of Dynamical Systems. He is also (co-)editor of several large volumes, Handbook of Dynamical Systems, 1A and 1B, and The Collected Works of Anatole Katok, Volumes 1 and 2. He is Fellow and the Secretary of the American Mathematical Society.

    • Andrey Gogolev , Ohio State University

      Andrey Gogolev is a Professor of Mathematics at The Ohio State University, USA. He received his PhD from Pennsylvania State University in 2009. His primary research interest is smooth dynamics with hyperbolic behavior. He serves on the editorial board of Journal of Modern Dynamics.

    • Yakov Pesin , Pennsylvania State University

      Yakov Pesin is Distinguished Professor of Mathematics at Pennsylvania State University, USA. He is director of the Anatole Katok Center for Dynamical Systems and Geometry, a member of the American Academy of Arts and Sciences, a member of the European Academy (Academia Europea), a fellow of the American Mathematical Society, and an editor of the journal Ergodic Theory and Dynamical Systems. He received his PhD in mathematics from Gorky State University in 1979. He has (co)authored six books covering smooth dynamics, ergodic theory, dimension theory, and fractal geometry, and a dozen surveys on these topics.