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Modern Dynamical Systems and Applications

Modern Dynamical Systems and Applications

$181.00 (Z)

Michael Brin, Boris Hasselblatt, Yakov Pesin, Vitaly Bergelson, Alex Gorodnik, Melanie Bertelson, Michael Gromov, Michael Boyle, Jack Wagoner, Patrick Eberlein, Renato Feres, B. Host, Bryna Kra, Chao-Hui Lin, Daniel Rudolph, Herbert Abels, Gregory Margulis, Klaus Schmidt, Ralf Spatzier, Serge Tabachnikov, Alexander Blokh, Chris Cleveland, Michal Misiurewicz, Jairo Bochi, Marcelo Vianam, Christina Bonatti, John Franks, Michael Brin, Dmitri Burago, S. Ivanov, Bassam Fayad, Dmitry Dolgopyat, Jorg Schmeling, Huyi Hu, Yakov Pesin, Anna Talitskaya, Michael Jakobson, Oliver Jenkinson, Mark Pollicott, Yuri Kifer, Sheldon Newhouse, Domokos Szasz, Tamas Varju, Jean-Christophe Yoccoz
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  • Date Published: August 2004
  • availability: In stock
  • format: Hardback
  • isbn: 9780521840736

$181.00 (Z)
Hardback

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About the Authors
  • Presenting a wide cross-section of current research in the theory of dynamical systems, this collection consists of articles by leading researchers (and several Fields medallists) in a variety of specialties. Surveys featuring new results, as well as research papers, are included because of their potentially high impact. Major areas covered include hyperbolic dynamics, elliptic dynamics, mechanics, geometry, ergodic theory, group actions, rigidity, and applications. The target audience is dynamicists, as well as mathematicians from other disciplines.

    • Covers articles by leading experts in the field and covers broad scope of modern dynamical systems theory
    • A coherent and valuable collection of up-to-date summaries of the states of the field
    • Includes surveys of new results
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    Product details

    • Date Published: August 2004
    • format: Hardback
    • isbn: 9780521840736
    • length: 474 pages
    • dimensions: 262 x 188 x 38 mm
    • weight: 1.035kg
    • availability: In stock
  • Table of Contents

    1. Introduction Michael Brin, Boris Hasselblatt and Yakov Pesin
    Part I. Ergodic Theory, Rigidity, Geometry:
    2. Weakly mixing actions of general groups: a brief survey and an example Vitaly Bergelson and Alex Gorodnik
    3. Dynamical Morse entropy Melanie Bertelson and Michael Gromov
    4. Positive k-theory and symbolic dynamics Michael Boyle and Jack Wagoner
    5. Geometry of 2-step nilpotent Lie groups with a left invariant metric Patrick Eberlein
    6. A differential-geometric view of normal forms of contractions Renato Feres
    7. Averaging along cubes B. Host and Bryna Kra
    8. Sections for semiflows and Kakutani shift equivalence Chao-Hui Lin and Daniel Rudolph
    9. Coarsely geodesic metrics on reductive groups Herbert Abels and Gregory Margulis
    10. Algebraic Zd-actions on zero-dimensional compact Abelian groups Klaus Schmidt
    11. An invitation to rigidity theory Ralf Spatzier
    12. Remarks on magnetic flows and magnetic billiards, Finsler metrics and a magnetic analog of Hilbert's fourth problem Serge Tabachnikov
    Part II. Hyperbolic Dynamics:
    13. Expanding polymodials Alexander Blokh, Chris Cleveland and Michal Misiurewicz
    14. Lyapunov exponents: how frequently are dynamical systems hyperbolic? Jairo Bochi and Marcelo Viana
    15. A Hölder continuous vector field tangent to many foliations Christina Bonatti and John Franks
    16. On partially hyperbolic diffeomorphisms of 3-manifolds with commutative fundamental groups Michael Brin, Dmitri Burago and S. Ivanov
    17. Prelude to a kiss Dmitry Dolgopyat
    18. Nonuniform hpyerbolicity and elliptic dynamics Bassam Fayad
    19. Dimension product structure of hyperbolic sets Boris Hasselblatt and Jorg Schmeling
    20. Every compact manifold carries a hyperbolic Bernoulli flow Huyi Hu, Yakov Pesin and Anna Talitskaya
    21. Parameter choice for families of maps with many critical points Michael Jakobson
    22. Entropy, exponents and invariant densities for hyperbolic systems: dependence and computation Oliver Jenkinson and Mark Pollicott
    23. Some recent advances in averaging Yuri Kifer
    24. Bootstrap of regularity for integrable solutions of cohomology equations Rafael de la Llave
    25. Cone-fields, domination, and hyperbolicity Sheldon Newhouse
    26. Markov towers and stochastic properties of billiards Domokos Szasz and Tamas Varju
    27. Some questions and remarks about SL(2,R) cocycles Jean-Christophe Yoccoz.

  • Editors

    Michael Brin, University of Maryland, College Park

    Boris Hasselblatt, Tufts University, Massachusetts

    Yakov Pesin, Pennsylvania State University

    Contributors

    Michael Brin, Boris Hasselblatt, Yakov Pesin, Vitaly Bergelson, Alex Gorodnik, Melanie Bertelson, Michael Gromov, Michael Boyle, Jack Wagoner, Patrick Eberlein, Renato Feres, B. Host, Bryna Kra, Chao-Hui Lin, Daniel Rudolph, Herbert Abels, Gregory Margulis, Klaus Schmidt, Ralf Spatzier, Serge Tabachnikov, Alexander Blokh, Chris Cleveland, Michal Misiurewicz, Jairo Bochi, Marcelo Vianam, Christina Bonatti, John Franks, Michael Brin, Dmitri Burago, S. Ivanov, Bassam Fayad, Dmitry Dolgopyat, Jorg Schmeling, Huyi Hu, Yakov Pesin, Anna Talitskaya, Michael Jakobson, Oliver Jenkinson, Mark Pollicott, Yuri Kifer, Sheldon Newhouse, Domokos Szasz, Tamas Varju, Jean-Christophe Yoccoz

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