Topological Dynamical Systems

1 - Preface [Seite 5]
2 - Notation [Seite 9]
3 - 0 Introduction [Seite 17]
3.1 - 0.1 Definition and a (very brief) historical overview [Seite 17]
3.2 - 0.2 Continuous vs. discrete time [Seite 19]
3.3 - 0.3 The dynamical systems point of view [Seite 23]
3.4 - 0.4 Examples [Seite 25]
4 - 1 Basic notions [Seite 33]
4.1 - 1.1 Invariant and periodic points [Seite 33]
4.2 - 1.2 Invariant sets [Seite 39]
4.3 - 1.3 Transitivity [Seite 44]
4.4 - 1.4 Limit sets [Seite 49]
4.5 - 1.5 Topological conjugacy and factor mappings [Seite 51]
4.6 - 1.6 Equicontinuity and weak mixing [Seite 60]
4.7 - 1.7 Miscellaneous examples [Seite 73]
5 - 2 Dynamical systems on the real line [Seite 89]
5.1 - 2.1 Graphical iteration [Seite 89]
5.2 - 2.2 Existence of periodic orbits [Seite 96]
5.3 - 2.3 The truncated tent map [Seite 100]
5.4 - 2.4 The double of a mapping [Seite 103]
5.5 - 2.5 The Markov graph of a periodic orbit in an interval [Seite 107]
5.6 - 2.6 Transitivity of mappings of an interval [Seite 117]
6 - 3 Limit behaviour [Seite 133]
6.1 - 3.1 Limit sets and attraction [Seite 133]
6.2 - 3.2 Stability [Seite 142]
6.3 - 3.3 Stability and attraction for periodic orbits [Seite 148]
6.4 - 3.4 Asymptotic stability in locally compact spaces [Seite 159]
6.5 - 3.5 The structure of (asymptotically) stable sets [Seite 169]
7 - 4 Recurrent behaviour [Seite 181]
7.1 - 4.1 Recurrent points [Seite 181]
7.2 - 4.2 Almost periodic points and minimal orbit closures [Seite 185]
7.3 - 4.3 Non-wandering points [Seite 191]
7.4 - 4.4 Chain-recurrence [Seite 198]
7.5 - 4.5 Asymptotic stability and basic sets [Seite 213]
8 - 5 Shift systems [Seite 234]
8.1 - 5.1 Notation and terminology [Seite 234]
8.2 - 5.2 The shift mapping [Seite 239]
8.3 - 5.3 Shift spaces [Seite 242]
8.4 - 5.4 Factor maps [Seite 252]
8.5 - 5.5 Subshifts and graphs [Seite 260]
8.6 - 5.6 Recurrence, almost periodicity and mixing [Seite 269]
9 - 6 Symbolic representations [Seite 298]
9.1 - 6.1 Topological partitions [Seite 298]
9.2 - 6.2 Expansive systems [Seite 309]
9.3 - 6.3 Applications [Seite 318]
10 - 7 Erratic behaviour [Seite 341]
10.1 - 7.1 Stability revisited [Seite 341]
10.2 - 7.2 Chaos(1): sensitive systems [Seite 352]
10.3 - 7.3 Chaos(2): scrambled sets [Seite 358]
10.4 - 7.4 Horseshoes for interval maps [Seite 371]
10.5 - 7.5 Existence of a horseshoe [Seite 381]
11 - 8 Topological entropy [Seite 394]
11.1 - 8.1 The definition [Seite 394]
11.2 - 8.2 Independence of the metric [Seite 403]
11.3 - 8.3 Maps on intervals and circles [Seite 407]
11.4 - 8.4 The definition with covers [Seite 410]
11.5 - 8.5 Miscellaneous results [Seite 418]
11.6 - 8.6 Positive entropy and horseshoes for interval maps [Seite 422]
12 - A Topology [Seite 439]
12.1 - A.1 Elementary notions [Seite 439]
12.2 - A.2 Compactness [Seite 442]
12.3 - A.3 Continuous mappings [Seite 444]
12.4 - A.4 Convergence [Seite 446]
12.5 - A.5 Subspaces, products and quotients [Seite 448]
12.6 - A.6 Connectedness [Seite 450]
12.7 - A.7 Metric spaces [Seite 453]
12.8 - A.8 Baire category [Seite 460]
12.9 - A.9 Irreduciblemappings [Seite 462]
12.10 - A.10 Miscellaneous results [Seite 465]
13 - B The Cantor set [Seite 469]
13.1 - B.1 The construction [Seite 469]
13.2 - B.2 Proof of Brouwer's Theorem [Seite 472]
13.3 - B.3 Cantor spaces [Seite 477]
14 - C Hints to the Exercises [Seite 481]
15 - Literature [Seite 497]
16 - Index [Seite 501]