Differentiable dynamical systems: an introduction to structural stability and hyperbolicity
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, Rhode Island
American Mathematical Society
[2016]
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| Series: | Graduate studies in mathematics
173 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | xi, 192 Seiten Diagramme |
| ISBN: | 9781470427993 |
Staff View
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Record in the Search Index
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| adam_text | Titel: Differentiable dynamical systems
Autor: Wen, Lan
Jahr: 2016
Contents Preface ix Chapter 1. Basics of dynamical systems 1 §1.1. Basic concepts 4 §1.2. Topological conjugacy and structural stability 10 §1.3. Circle homeomorphisms 14 §1.4. Conley’s fundamental theorem of dynamical systems 18 Exercises 22 Chapter 2. Hyperbolic fixed points 25 §2.1. Hyperbolic linear isomorphisms 25 §2.2. Persistence of hyperbolic fixed points 29 §2.3. Persistence of hyperbolicity for a fixed point 34 §2.4. Hartman-Grobman theorem 41 §2.5. The local stable manifold for a hyperbolic fixed point 45 Exercises 54 Chapter 3. Horseshoes, toral automorphisms, and solenoids 57 §3.1. Symbolic dynamics 57 §3.2. Smale horseshoe 60 §3.3. Anosov toral automorphisms 66 §3.4. The solenoid attractor 70 Exercises 73 vii
75 75 83 89 95 117 128 134 139 139 145 147 150 154 157 157 158 166 168 172 180 181 189 viii Chapter 4. Hyperbolic sets §4.1. The concept of hyperbolic set §4.2. Persistence of hyperbolicity for an invariant set §4.3. Smoothness in Lemma 2.17 and Theorem 2.18 §4.4. Stable manifolds of hyperbolic sets §4.5. Structural stability of hyperbolic sets §4.6. The shadowing lemma Exercises Chapter 5. Axiom A, no-cycle condition, and il-stability §5.1. Spectral decomposition and Axiom A §5.2. Cycle and Q-explosion §5.3. No-cycle and fi-stability §5.4. Equivalent descriptions Exercises Chapter 6. Quasi-hyperbolicity and linear transversality §6.1. The simplest setting §6.2. Quasi-hyperbolicity §6.3. Linear transversality §6.4. Applications §6.5. A glimpse of the stability conjectures Exercises Bibliography Index
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| discipline | Mathematik |
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| indexdate | 2024-07-10T07:33:28Z |
| institution | BVB |
| isbn | 9781470427993 |
| language | English |
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| physical | xi, 192 Seiten Diagramme |
| publishDate | 2016 |
| publishDateSearch | 2016 |
| publishDateSort | 2016 |
| publisher | American Mathematical Society |
| record_format | marc |
| series | Graduate studies in mathematics |
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| spelling | Wen, Lan 1946- Verfasser (DE-588)1113541423 aut Differentiable dynamical systems an introduction to structural stability and hyperbolicity Lan Wen Providence, Rhode Island American Mathematical Society [2016] xi, 192 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier Graduate studies in mathematics 173 Hyperbolizität (DE-588)4710615-3 gnd rswk-swf Differenzierbares dynamisches System (DE-588)4137931-7 gnd rswk-swf Differenzierbares dynamisches System (DE-588)4137931-7 s Hyperbolizität (DE-588)4710615-3 s DE-604 Graduate studies in mathematics 173 (DE-604)BV009739289 173 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029136664&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Wen, Lan 1946- Differentiable dynamical systems an introduction to structural stability and hyperbolicity Graduate studies in mathematics Hyperbolizität (DE-588)4710615-3 gnd Differenzierbares dynamisches System (DE-588)4137931-7 gnd |
| subject_GND | (DE-588)4710615-3 (DE-588)4137931-7 |
| title | Differentiable dynamical systems an introduction to structural stability and hyperbolicity |
| title_auth | Differentiable dynamical systems an introduction to structural stability and hyperbolicity |
| title_exact_search | Differentiable dynamical systems an introduction to structural stability and hyperbolicity |
| title_full | Differentiable dynamical systems an introduction to structural stability and hyperbolicity Lan Wen |
| title_fullStr | Differentiable dynamical systems an introduction to structural stability and hyperbolicity Lan Wen |
| title_full_unstemmed | Differentiable dynamical systems an introduction to structural stability and hyperbolicity Lan Wen |
| title_short | Differentiable dynamical systems |
| title_sort | differentiable dynamical systems an introduction to structural stability and hyperbolicity |
| title_sub | an introduction to structural stability and hyperbolicity |
| topic | Hyperbolizität (DE-588)4710615-3 gnd Differenzierbares dynamisches System (DE-588)4137931-7 gnd |
| topic_facet | Hyperbolizität Differenzierbares dynamisches System |
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