Dynamics of Topologically Generic

Introduction Attractors and chain recurrence Periodic decompositions and adding machines Semicontinuity and homogeneity Crushing arguments Topological horseshoes Generic homeomorphisms Almost equicontinuity Cantor sets The circle Crushing the chain recurrent set Generic homeomorphisms on manifolds Generic mappings on manifolds Bibliography Index

Introduction

1

(1)

Overview

1

(1)

Description of results

2

(3)

Brief remarks about techniques

5

(1)

Comparison with the smooth case

6

(1)

Standing notation

7

(1)

Road map

8

(1)

Comments

8

(3)

Attractors and Chain Recurrence

11

(10)

Chain recurrence

11

(2)

Attractors

13

(2)

Attractor-repellor pairs

15

(1)

Initial and terminal chain components

16

(1)

The space(s) of chain components

17

(1)

Summary

18

(3)

Periodic Decompositions and Adding Machines

21

(10)

Periodic decompositions

21

(1)

The sets II∞ and II∞,∞

22

(1)

Adding machines

23

(2)

Decompositions of u type

25

(3)

Periodicity conditions

28

(3)

Semicontinuity and Homogeneity

31

(8)

Semicontinuity

31

(1)

Prolongation

32

(1)

The automorphism group

33

(2)

Homogeneity conditions

35

(1)

Showing Ω(ƒ) = C(ƒ)

36

(3)

Crushing Arguments

39

(14)

Sponges

39

(5)

Crushing

44

(9)

Topological Horseshoes

53

(12)

Connected successions of subsets

53

(1)

Topological horseshoes

54

(3)

Perturbing to a horseshoe

57

(8)

Generic Homeomorphisms

65

(14)

The classes H1 and H1,s

65

(5)

The class H,s

70

(3)

Dynamic isolation

73

(1)

Attractor boundaries are quasi-attractors

73

(2)

Shift extensions and the class H4

75

(4)

Almost Equicontinuity

79

(6)

Chain continuity

81

(4)

Cantor Sets

85

(12)

Aperiodicity and the class H5

85

(1)

The class H6

86

(3)

Rohlin property

89

(1)

The class H3,c

90

(7)

The Circle

97

(10)

Background

97

(2)

The class H1 on S1

99

(4)

Relative Rohlin property

103

(4)

Crushing the Chain Recurrent Set

107

(8)

Generic Homeomorphisms on Manifolds

115

(6)

The class H8

115

(1)

The class Hman

116

(1)

Anosov homeomorphisms

116

(5)

Generic Mappings on Manifolds

121

(4)

Bibliography

125

(4)

Index

129

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Dynamics of Topologically Generic Homeomorphisms

Summary

Table of Contents

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