Introduction to dynamical systems:
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge [u.a.]
Cambridge Univ. Press
2009
|
| Edition: | 1. publ., transferred to digital print. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Includes bibliographical references and index. |
| Physical Description: | XII, 240 S. graph. Darst. |
| ISBN: | 0521808413 9780521808415 |
Staff View
MARC
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| 245 | 1 | 0 | |a Introduction to dynamical systems |c Michael Brin ; Garrett Stuck |
| 250 | |a 1. publ., transferred to digital print. | ||
| 264 | 1 | |a Cambridge [u.a.] |b Cambridge Univ. Press |c 2009 | |
| 300 | |a XII, 240 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 500 | |a Includes bibliographical references and index. | ||
| 650 | 0 | 7 | |a Differenzierbares dynamisches System |0 (DE-588)4137931-7 |2 gnd |9 rswk-swf |
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Record in the Search Index
| _version_ | 1804141146444660736 |
|---|---|
| adam_text | Contents
Introduction page
xi
1
Examples and Basic Concepts
1
1.1
The Notion of a Dynamical System
1
1.2
Circle Rotations
3
1.3
Expanding Endomorphisms of the Circle
5
1.4
Shifts and Subshifts
7
1.5
Quadratic Maps
9
1.6
The Gauss Transformation
11
1.7
Hyperbolic
Toral
Automorphisms
13
1.8
The Horseshoe
15
1.9
The Solenoid
17
1.10
Flows and Differential Equations
19
1.11
Suspension and Cross-Section
21
1.12
Chaos and Lyapunov Exponents
23
1.13
Attractors
25
2
Topological Dynamics
28
2.1
Limit Sets and Recurrence
28
2.2
Topological Transitivity
31
2.3
Topological Mixing
33
2.4
Expansiveness
35
2.5
Topological Entropy
36
2.6
Topological Entropy for Some Examples
41
2.7
Equicontinuity, Distality, and Proximality
45
2.8
Applications of Topological Recurrence to
Ramsey Theory
48
3
Symbolic Dynamics
54
3.1
Subshifts and Codes
55
3.2
Subshifts of Finite Type
56
3.3
The Perron-Frobenius Theorem
57
3.4
Topological Entropy and the
Zeta
Function of an SFT
60
3.5
Strong Shift Equivalence and Shift Equivalence
62
3.6
Substitutions
64
3.7
Sofie
Shifts
66
3.8
Data Storage
67
4
Ergodic Theory
69
4.1
Measure-Theory Preliminaries
69
4.2
Recurrence
71
4.3
Ergodicity and Mixing
73
4.4
Examples
77
4.5
Ergodic Theorems
80
4.6
Invariant Measures for Continuous Maps
85
4.7
Unique Ergodicity and Weyl s Theorem
87
4.8
The Gauss Transformation Revisited
90
4.9
Discrete Spectrum
94
4.10
Weak Mixing
97
4.11
Applications of Measure-Theoretic Recurrence
to Number Theory
101
4.12
Internet Search
103
5
Hyperbolic Dynamics
106
5.1
Expanding Endomorphisms Revisited
107
5.2
Hyperbolic Sets
108
5.3
6-Orbits
110
5.4
Invariant Cones
114
5.5
Stability ot Hyperbolic Sets
117
5.6
Stable and Unstable Manifolds
118
5.7
Inclination Lemma
122
5.8
Horseshoes and Transverse Homoclinic Points
124
5.9
Local Product Structure and Locally Maximal
Hyperbolic Sets
128
5.10
Anosov Diffeomorpnisms
130
5.11
Axiom A and Structural Stability
133
5.12
Markov Partitions
134
5.13
Appendix: Differentiable Manifolds
137
Contents
6 Ergodicity
of Anosov Diffeomorphisms
6.1
Holder Continuity of the Stable and Unstable
Distributions
6.2
Absolute Continuity of the Stable and Unstable
Foliations
6.3
Proof of Ergodicity
Ί
Low-Dimensional Dynamics
7.1
Circle Homeomorphisms
7.2
Circle Diffeomorphisms
7.3
The Sharkovsky Theorem
7.4
Combinatorial Theory of Piecewise-Monotone
Mappings
7.5
The Schwarzian Derivative
7.6
Real Quadratic Maps
7.7
Bifurcations of Periodic Points
7.8
The
Feigenbaum
Phenomenon
ΰ
Complex Dynamics
8.1
Complex Analysis on the Riemann Sphere
8.2
Examples
8.3
Normal Families
8.4
Periodic Points
8.5
The Julia Set
8.6
The Mandelbrot Set
9
Measure-Theoretic Entropy
9.1
Entropy of a Partition
9.2
Conditional Entropy
9.3
Entropy of a Measure-Preserving Transformation
9.4
Examples of Entropy Calculation
9.5
Variational Principle
Bibliography
Index
|
| any_adam_object | 1 |
| author | Brin, Michael 1948- Stuck, Garrett |
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| building | Verbundindex |
| bvnumber | BV036085917 |
| classification_rvk | SK 350 |
| ctrlnum | (OCoLC)634134108 (DE-599)BVBBV036085917 |
| discipline | Mathematik |
| edition | 1. publ., transferred to digital print. |
| format | Book |
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| id | DE-604.BV036085917 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T22:11:14Z |
| institution | BVB |
| isbn | 0521808413 9780521808415 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-018976878 |
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| physical | XII, 240 S. graph. Darst. |
| publishDate | 2009 |
| publishDateSearch | 2009 |
| publishDateSort | 2009 |
| publisher | Cambridge Univ. Press |
| record_format | marc |
| spelling | Brin, Michael 1948- Verfasser (DE-588)113096062 aut Introduction to dynamical systems Michael Brin ; Garrett Stuck 1. publ., transferred to digital print. Cambridge [u.a.] Cambridge Univ. Press 2009 XII, 240 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Includes bibliographical references and index. Differenzierbares dynamisches System (DE-588)4137931-7 gnd rswk-swf Differenzierbares dynamisches System (DE-588)4137931-7 s DE-604 Stuck, Garrett Verfasser aut Digitalisierung UB Passau application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018976878&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Brin, Michael 1948- Stuck, Garrett Introduction to dynamical systems Differenzierbares dynamisches System (DE-588)4137931-7 gnd |
| subject_GND | (DE-588)4137931-7 |
| title | Introduction to dynamical systems |
| title_auth | Introduction to dynamical systems |
| title_exact_search | Introduction to dynamical systems |
| title_full | Introduction to dynamical systems Michael Brin ; Garrett Stuck |
| title_fullStr | Introduction to dynamical systems Michael Brin ; Garrett Stuck |
| title_full_unstemmed | Introduction to dynamical systems Michael Brin ; Garrett Stuck |
| title_short | Introduction to dynamical systems |
| title_sort | introduction to dynamical systems |
| topic | Differenzierbares dynamisches System (DE-588)4137931-7 gnd |
| topic_facet | Differenzierbares dynamisches System |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018976878&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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