Spaces of Dynamical Systems / Sergei Yu. Pilyugin.

Format:

Book

Author/Creator:

Pilyugin, Sergei Yu., Author.

Series:

De Gruyter studies in mathematical physics ; 3.

De Gruyter Studies in Mathematical Physics ; 3

Language:

English

Subjects (All):

Dynamics.

Physical Description:

1 online resource (xv, 229 pages) : illustrations.

Edition:

2. rev. and exten. edition

Place of Publication:

Berlin ; Boston : De Gruyter, [2019]

Language Note:

In English.

Summary:

The De Gruyter Studies in Mathematical Physics are devoted to the publication of monographs and high-level texts in mathematical physics. They cover topics and methods in fields of current interest, with an emphasis on didactical presentation. The series will enable readers to understand, apply and develop further, with sufficient rigor, mathematical methods to given problems in physics. For this reason, works with a few authors are preferred over edited volumes. The works in this series are aimed at advanced students and researchers in mathematical and theoretical physics. They can also serve as secondary reading for lectures and seminars at advanced levels.

Contents:

Frontmatter

Contents

Preface to the first edition

Preface to the second edition

List of main symbols

1. Dynamical systems

2. Topologies on spaces of dynamical systems

3. Equivalence relations

4. Hyperbolic fixed point

5. Hyperbolic rest point and hyperbolic closed trajectory

6. Transversality

7. Hyperbolic sets

8. Anosov diffeomorphisms

9. Smale's horseshoe and chaos

10. Closing lemma

11. C0-generic properties of dynamical systems

12. Shadowing of pseudotrajectories in dynamical systems

13. Invariant measures

A. Scheme of the proof of the Mañé theorem

B. Lectures on selected chapters of the history of differential equations and dynamical systems

Bibliography

Index

Notes:

Description based on online resource; title from PDF title page (publisher's Web site, viewed 06. Apr 2020)

ISBN:

3-11-065399-0

3-11-065716-3

OCLC:

1114811647