This updated revision conveys the modern theory of dynamical systems in a comprehensible and didactically structure based on many years of teaching. The work covers the current research of topological dynamics, structural stability, chaotic dynamics
Author(s): Sergei Yu. Pilyugin
Series: De Gruyter Studies in Mathematical Physics 3
Edition: 2
Publisher: De Gruyter
Year: 2019
Language: English
Pages: 260
Cover......Page 1
Spaces of
Dynamical
Systems
......Page 5
© 2019......Page 6
Contents
......Page 7
Preface to the first edition......Page 11
Preface to the second edition......Page 15
List of main symbols......Page 17
1 Dynamical systems......Page 19
2 Topologies on spaces of dynamical systems......Page 34
3 Equivalence relations......Page 44
4 Hyperbolic fixed point......Page 55
5 Hyperbolic rest point and hyperbolic closed
trajectory......Page 84
6 Transversality......Page 95
7 Hyperbolic sets......Page 108
8 Anosov diffeomorphisms......Page 134
9 Smale’s horseshoe and chaos......Page 141
10 Closing lemma......Page 149
11 C0-generic properties of dynamical systems......Page 154
12 Shadowing of pseudotrajectories in dynamical
systems......Page 171
13 Invariant measures......Page 192
A.
Scheme of the proof of the Mañé theorem......Page 214
B.
Lectures on selected chapters of the history of
differential equations and dynamical systems......Page 224
Bibliography......Page 254
Index......Page 257
