Details

Autor(en) / Beteiligte

• Hasselblatt, Boris
• Katok, A. B

Titel

Handbook of dynamical systems. Vol. 1B

Auflage

1st ed

Beschreibungen/Notizen

• Description based upon print version of record.
• Includes bibliographical references and indexes.
• Preface; List of Contributors; Contents; Contents of Volume 1A; Partially Hyperbolic Dynamical Systems; Introduction; Definitions and examples; Filtrations of stable and unstable foliations; Central foliations; Intermediate foliations; Failure of absolute continuity; Accessibility and stable accessibility; The Pugh-Shub ergodicity theory; Partially hyperbolic attractors; Acknowledgements; References; Smooth Ergodic Theory and Nonuniformly Hyperbolic Dynamics; Introduction; Lyapunov exponents of dynamical systems; Examples of systems with nonzero exponents
• Lyapunov exponents associated with sequences of matricesCocycles and Lyapunov exponents; Regularity and Multiplicative Ergodic Theorem; Cocycles over smooth dynamical systems; Methods for estimating exponents; Local manifold theory; Global manifold theory; Absolute continuity; Smooth invariant measures; Metric entropy; Genericity of systems with nonzero exponents; SRB-measures; Hyperbolic measures I: Topological properties; Hyperbolic measures II: Entropy and dimension; Geodesic flows on manifolds without conjugate points; Dynamical systems with singularities: The conservative case
• Hyperbolic attractors with singularitiesAcknowledgements; Appendix A. Decay of correlations, by Omri Sarig; References; Stochastic-Like Behaviour in Nonuniformly Expanding Maps; Introduction; Basic definitions; Markov structures; Uniformly expanding maps; Almost uniformly expanding maps; One-dimensional maps with critical points; General theory of nonuniformly expanding maps; Existence of nonuniformly expanding maps; Conclusion; Acknowledgements; References; Homoclinic Bifurcations, Dominated Splitting, and Robust Transitivity; Introduction; A weaker form of hyperbolicity: Dominated splitting
• Homoclinic tangenciesSurface diffeomorphisms; Nonhyperbolic robustly transitive systems; Flows and singular splitting; References; Random Dynamics; Introduction; Basic structures of random transformations; Smooth RDS: Invariant manifolds; Relations between entropy, exponents and dimension; Thermodynamic formalism and its applications; Random perturbations of dynamical systems; Concluding remarks; References; An Introduction to Veech Surfaces; Introduction to Veech surfaces; State of the art; References; Ergodic Theory of Translation Surfaces
• Three definitions of translation surface or flat surface and examplesSpaces of translations surfaces and Riemann surfaces; SL(2,R)-action and invariant measures; Ergodicity of flows defined by translation surfaces; Further results on unique ergodicity; Boshernitzan's Theorem and sketch of proof of Theorem 3; Further results on dynamics of actions of subgroups of SL(2,R); Acknowledgements; References; On the Lyapunov Exponents of the Kontsevich-Zorich Cocycle; Introduction; Elements of Teichmüller theory; The Kontsevich-Zorich cocycle; Variational formulas; Bounds on the exponents
• The determinant locus
• This second half of Volume 1 of this Handbook follows Volume 1A, which was published in 2002. The contents of these two tightly integrated parts taken together come close to a realization of the program formulated in the introductory survey "Principal Structures? of Volume 1A.The present volume contains surveys on subjects in four areas of dynamical systems: Hyperbolic dynamics, parabolic dynamics, ergodic theory and infinite-dimensional dynamical systems (partial differential equations).. Written by experts in the field.. The coverage of ergodic theory in these two parts o
• English