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9780521840736

Modern Dynamical Systems and Applications

by
  • ISBN13:

    9780521840736

  • ISBN10:

    0521840732

  • Format: Hardcover
  • Copyright: 2004-08-16
  • Publisher: Cambridge University Press

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Summary

This volume presents a wide cross section of current research in the theory of dynamical systems and contains articles by leading researchers, including several Fields medalists, in a variety of specialties. These are surveys, usually with new results included, as well as research papers that are included because of their potentially high impact. Major areas covered include hyperbolic dynamics, elliptic dynamics, mechanics, geometry, ergodic theory, group actions, rigidity, applications. The target audience includes dynamicists, who will find new results in their own specialty as well as surveys in others, and mathematicians from other disciplines who look for a sample of current developments in ergodic theory and dynamical systems.

Table of Contents

Introduction xi
Michael Brin, Boris Hasselblatt, Yakov Pesin
Part I. Ergodic Theory, Rigidity, Geometry
Weakly mixing actions of general groups: a brief survey and an example
3(24)
Vitaly Bergelson, Alex Gorodnik
Dynamical Morse entropy
27(18)
Melanie Bertelson, Micahel Gromov
Positive k-theory and symbolic dynamcis
45(22)
Michael Boyle, Jack Wagoner
Geometry of 2-step nilpotent Lie groups with a left invariant metric
67(36)
Patrick Eberlein
A differential-geometric view of normal forms of contractions
103(20)
Renato Feres
Averaging along cubes
123(22)
B. Host and Bryna Kra
Sections for Semiflows and Kakutani Shift Equivalence
145(18)
Chao-Hui Lin, Daniel Rudolph
Coarsely geodesic metrics on reductive groups
163(22)
Herbert Abels, Gregory Margulis
Algebraic Zd-Actions on Zero-dimensional compact Abelian Groups
185(26)
Klaus Schmidt
An Invitation to Rigidity Theory
211(22)
Ralf Spatzier
Remarks on magnetic flows and magnetic billiards, Finsler metrics and a magnetic analog of Hilbert's fourth problem
233(20)
Serge Tabachnikov
Part II. Hyperbolic Dynamics
Expanding polymodials
253(18)
Alexander Blokh, Chris Cleveland, Michal Misiurewicz
Lyapunov exponents: How frequently are dynamical systems hyperbolic?
271(28)
Jairo Bochi, Marcelo Viana
A Holder continuous vector field tangent to many foliations
299(8)
Christian Bonatti, John Franks
On Partially Hyperbolic Diffeomorphisms of 3-manifolds with commutative Fundamental groups
307(6)
Michael Brin, Dmitri Burago, S. Ivanov
Prelude to a kiss
313(12)
Dmitry Dolgopyat
Nonuniform hyperbolicity and elliptic dynamics
325(6)
Bassam Fayad
Dimension product structure of Hyperbolic sets
331(16)
Boris Hasselblatt, Jorg Schmeling
Every Compact manifold carries a hyperbolic Bernoulli flow
347(12)
Huyi Hu, Yakov Pesin, Anna Talitskaya
Parameter choice for families of maps with many critical points
359(26)
Michael Jakobson
Entropy, Exponents and Invariant Densities for hyperbolic systems: Dependence and Computation 365
Oliver Jenkinson, Mark Pollicott
Some recent advances in averaging
385(34)
Yuri Kifer
Bootstrap of regularity for integable solutions of cohomology equations 405 Rafael de la Llave Cone-fields, domination, and hyperbolicity
419(14)
Sheldon Newhouse
Markov Towers and Stochastic Properties of Billiards
433(14)
Domokos Szasz, Tamas Varju
Some questions and remarks about SL(2,R) cocycles
447
Jean-Christophe Yoccoz

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The New copy of this book will include any supplemental materials advertised. Please check the title of the book to determine if it should include any access cards, study guides, lab manuals, CDs, etc.

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