Dynamics Reported: Expositions in Dynamical Systems(4 Dynamics Reported. New Series)

This book contains four contributions in the field of dynamical systems. The topics treated are also related to topology, Hamiltonian systems and stochastics. All the authors give a careful readable presentation of recent research results, addressed to graduate students and researchers in these fields; the book is also suitable as a text for graduate level seminars in dynamical systems.

Table of Contents:
The "Spectral" Decomposition for One–Dimensional Maps.- 1. Introduction and Main Results.- 2. Technical Lemmas.- 3. Solenoidal Sets.- 4. Basic Sets.- 5. The Decomposition.- 6. Limit Behavior for Maps Without Wandering Intervals.- 7. Topological Properties of the Sets Per f, ?(f) and ?(f).- 8. Transitive and Mixing Maps.- 9. Corollaries Concerning Periods of Cycles.- 10. Invariant Measures.- 11. Discussion of Some Recent Results of Block and Coven and Xiong Jincheng.- References.- A Constructive Theory of Lagrangian Tori and Computer-assisted Applications.- 1. Introduction.- 2. Quasi-Periodic Solutions and Invariant Tori for Lagrangian Systems: Algebraic Structure.- 3. Quasi-Periodic Solutions and Invariant Tori for Lagrangian Systems: Quantitative Analysis.- 4. KAM Algorithm.- 5. A KAM Theorem.- 6. Application of the KAM Algorithm to Problems with Parameters.- 7. Power Series Expansions and Estimate of the Error Term.- 8. Computer Assisted Methods.- 9. Applications: Three-Dimensional Phase Space Systems.- 10. Applications: Symplectic Maps.- Appendices.- References.- Ergodicity in Hamiltonian Systems.- 0. Introduction.- 1. A Model Problem.- 2. The Sinai Method.- 3. Proof of the Sinai Theorem.- 4. Sectors in a Linear Symplectic Space.- 5. The Space of Lagrangian Subspaces Contained in a Sector.- 6. Unbounded Sequences of Linear Monotone Maps.- 7. Properties of the System and the Formulation of the Results.- 8. Construction of the Neighborhood and the Coordinate System.- 9. Unstable Manifolds in the Neghborhood U.- 10. Local Ergodicity in the Smooth Case.- 11. Local Ergodicity in the Discontinous Case.- 12. Proof of Sinai Theorem.- 13. ‘Tail Bound’.- 14. Applications.- References.- Linearization of Random Dynamical Systems.- 1. Introduction.- 2. Random DifferenceEquations.- 3. Random Dynamical Systems.- 4. Local Results.- 5. Appendix.- References.