Dimension theory in dynamical systems: contemporary views and applications
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Chicago [u.a.]
Univ. of Chicago Press
1997
|
| Schriftenreihe: | Chicago lectures in mathematics series
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XI, 304 S. |
| ISBN: | 0226662217 0226662225 |
Internformat
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| 300 | |a XI, 304 S. | ||
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| 650 | 4 | |a Dynamique différentiable | |
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Datensatz im Suchindex
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| adam_text | Contents
Preface ix
Introduction 1
Part I: Caratheodory Dimension Characteristics
Chapter 1. General Caratheodory Construction 11
1. Caratheodory Dimension of Sets 12
2. Caratheodory Capacity of Sets 16
3. Caratheodory Dimension and Capacity of Measures 21
4. Coincidence of Caratheodory Dimension and Caratheodory Capacity
of Measures 28
5. Lower and Upper Bounds for Caratheodory Dimension of Sets;
Caratheodory Dimension Spectrum 31
Chapter 2. C Structures Associated with Metrics: Hausdorff
Dimension and Box Dimension 34
6. Hausdorff Dimension and Box Dimension of Sets 35
7. Hausdorff Dimension and Box Dimension of Measures; Pointwise
Dimension; Mass Distribution Principle 41
Chapter 3. C Structures Associated with Metrics and Measures:
Dimension Spectra 48
8. g Dimension and q Box Dimension of Sets 48
9. g Dimension and q Box Dimension of Measures 57
Appendix I: Hausdorff (Box) Dimension and q (Box) Dimension
of Sets and Measures in General Metric Spaces 61
Chapter 4. C Structures Associated with Dynamical Systems:
Thermodynamic Formalism 64
10. A Modification of the General Caratheodory Construction 65
11. Dimensional Definition of Topological Pressure; Topological and
Measure Theoretic Entropies 68
12. Non additive Thermodynamic Formalism 83
Appendix II: Variational Principle for Topological Pressure;
Symbolic Dynamical Systems; Bowen s Equation 87
Appendix III: An Example of Caratheodory Structure Generated
by Dynamical Systems 110
Part II: Applications to Dimension Theory and Dynamical Systems
Chapter 5. Dimension of Cantor like Sets and Symbolic Dynamics
117
13. Moran like Geometric Constructions with Stationary (Constant)
Ratio Coefficients 123
vii
viii Contents
14. Regular Geometric Constructions 133
15. Moran like Geometric Constructions with Non stationary Ratio
Coefficients 140
16. Geometric Constructions with Rectangles; Non coincidence of Box
Dimension and Hausdorff Dimension of Sets 153
Chapter 6. Multifractal Formalism 170
17. Correlation Dimension 174
18. Dimension Spectra: Hentschel Procaccia, Renyi, and /(a) Spectra;
Information Dimension 182
19. Multifractal Analysis of Gibbs Measures on Limit Sets of Geometric
Constructions 189
Chapter 7. Dimension of Sets and Measures Invariant under
Hyperbolic Systems 196
20. Hausdorff Dimension and Box Dimension of Conformal Repellers
for Smooth Expanding Maps 197
21. Multifractal Analysis of Gibbs Measures for Smooth Conformal
Expanding Maps 209
22. Hausdorff Dimension and Box Dimension of Basic Sets for Axiom
A Diffeomorphisms 227
23. Hausdorff Dimension of Horseshoes and Solenoids 238
24. Multifractal Analysis of Equilibrium Measures on Basic Sets of
Axiom A Diffeomorphisms 247
Appendix IV: A General Concept of Multifractal Spectra;
Multifractal Rigidity 259
Chapter 8. Relations between Dimension, Entropy, and Lyapunov
Exponents 270
25. Existence and Non existence of Pointwise Dimension for Invariant
Measures 271
26. Dimension of Measures with Non zero Lyapunov Exponents; The
Eckmann Ruelle Conjecture 279
Appendix V: Some Useful Facts 293
Bibliography 295
Index 301
|
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| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.352 |
| dewey-search | 515/.352 |
| dewey-sort | 3515 3352 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:18:48Z |
| institution | BVB |
| isbn | 0226662217 0226662225 |
| language | English |
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| physical | XI, 304 S. |
| publishDate | 1997 |
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| publisher | Univ. of Chicago Press |
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| series2 | Chicago lectures in mathematics series |
| spelling | Pesin, Yakov B. 1946- Verfasser (DE-588)129370533 aut Dimension theory in dynamical systems contemporary views and applications Yakov B. Pesin Chicago [u.a.] Univ. of Chicago Press 1997 XI, 304 S. txt rdacontent n rdamedia nc rdacarrier Chicago lectures in mathematics series Dimensietheorie gtt Dimension, Théorie de la (Topologie) Dynamique différentiable MEDIDA E INTEGRAÇÃO (ANÁLISE MATEMÁTICA) larpcal SISTEMAS DINAMICOS larpcal TEORIA DA DIMENSAO larpcal TOPOLOGIA larpcal Differentiable dynamical systems Dimension theory (Topology) Dimensionstheorie (DE-588)4149935-9 gnd rswk-swf Dynamisches System (DE-588)4013396-5 gnd rswk-swf Dimensionstheorie (DE-588)4149935-9 s Dynamisches System (DE-588)4013396-5 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008067686&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Pesin, Yakov B. 1946- Dimension theory in dynamical systems contemporary views and applications Dimensietheorie gtt Dimension, Théorie de la (Topologie) Dynamique différentiable MEDIDA E INTEGRAÇÃO (ANÁLISE MATEMÁTICA) larpcal SISTEMAS DINAMICOS larpcal TEORIA DA DIMENSAO larpcal TOPOLOGIA larpcal Differentiable dynamical systems Dimension theory (Topology) Dimensionstheorie (DE-588)4149935-9 gnd Dynamisches System (DE-588)4013396-5 gnd |
| subject_GND | (DE-588)4149935-9 (DE-588)4013396-5 |
| title | Dimension theory in dynamical systems contemporary views and applications |
| title_auth | Dimension theory in dynamical systems contemporary views and applications |
| title_exact_search | Dimension theory in dynamical systems contemporary views and applications |
| title_full | Dimension theory in dynamical systems contemporary views and applications Yakov B. Pesin |
| title_fullStr | Dimension theory in dynamical systems contemporary views and applications Yakov B. Pesin |
| title_full_unstemmed | Dimension theory in dynamical systems contemporary views and applications Yakov B. Pesin |
| title_short | Dimension theory in dynamical systems |
| title_sort | dimension theory in dynamical systems contemporary views and applications |
| title_sub | contemporary views and applications |
| topic | Dimensietheorie gtt Dimension, Théorie de la (Topologie) Dynamique différentiable MEDIDA E INTEGRAÇÃO (ANÁLISE MATEMÁTICA) larpcal SISTEMAS DINAMICOS larpcal TEORIA DA DIMENSAO larpcal TOPOLOGIA larpcal Differentiable dynamical systems Dimension theory (Topology) Dimensionstheorie (DE-588)4149935-9 gnd Dynamisches System (DE-588)4013396-5 gnd |
| topic_facet | Dimensietheorie Dimension, Théorie de la (Topologie) Dynamique différentiable MEDIDA E INTEGRAÇÃO (ANÁLISE MATEMÁTICA) SISTEMAS DINAMICOS TEORIA DA DIMENSAO TOPOLOGIA Differentiable dynamical systems Dimension theory (Topology) Dimensionstheorie Dynamisches System |
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