Lectures on partial hyperbolicity and stable ergodicity:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Zürich
European Mathematical Society
2004
|
| Series: | Zurich lectures in advanced mathematics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | VI, 122 S. graph. Darst. |
| ISBN: | 9783037190036 3037190035 |
Staff View
MARC
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| 100 | 1 | |a Pesin, Yakov B. |d 1946- |e Verfasser |0 (DE-588)129370533 |4 aut | |
| 245 | 1 | 0 | |a Lectures on partial hyperbolicity and stable ergodicity |c Yakov B. Pesin |
| 264 | 1 | |a Zürich |b European Mathematical Society |c 2004 | |
| 300 | |a VI, 122 S. |b graph. Darst. | ||
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| 650 | 7 | |a Teoria ergodica |2 larpcal | |
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| 650 | 4 | |a Foliations (Mathematics) | |
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Record in the Search Index
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|---|---|
| adam_text | Contents
1.
Introduction
..................................................... 1
2.
The Concept of Hyperbolicity
................................... 5
2.1.
Complete hyperbolicity (Anosov systems)
.................. 5
2.2.
Definition of partial hyperbolicity
.......................... 9
2.3.
Examples of partially hyperbolic systems
.................. 16
3.
The Mather Spectrum Theory
................................... 18
3.1.
Mather s spectrum of a diffeomorphism
.................... 18
3.2.
Stability of Mather s spectrum
............................ 20
3.3.
Holder continuity
.......................................... 24
4.
Stable and Unstable Foliations
.................................. 29
4.1.
Foliations
................................................. 29
4.2.
Stable Manifold theorem. The statement
.................. 30
4.3.
The
invariance
equation
................................... 31
4.4.
Local stable manifold theorem
............................. 33
4.5.
Construction of global manifolds
........................... 39
4.6.
Filtrations of foliations
.................................... 40
4.7.
The Inclination Lemma
.................................... 41
4.8.
Structural stability of Anosov diffeomorphisms
............. 45
5.
Central Foliations
............................................... 47
5.1.
Normal hyperbolicity
...................................... 47
5.2.
Local stability of normally hyperbolic manifolds
........... 49
5.3.
Integrability of the central foliation
........................ 50
5.4.
Central foliation and normal hyperbolicity
................. 55
5.5.
Robustness of the central foliation
......................... 55
5.6.
Weak integrability of the central foliation
.................. 62
6.
Intermediate Foliations
.......................................... 64
6.1.
Non-integrability of intermediate distributions
............. 64
6.2.
Invariant families of local manifolds
........................ 65
6.3.
Insufficient smoothness of intermediate foliations
.......... 70
7.
Absolute Continuity
............................................. 76
7.1.
The holonomy map
........................................ 76
7.2.
Absolute continuity of local manifolds
..................... 83
7.3.
Ergodicity of Anosov maps
................................ 85
7.4.
An example of a non-absolutely continuous foliation
....... 86
8.
Accessibility and Stable Accessibility
............................ 87
8.1.
The accessibility property
................................. 87
vi YA.
PEŞIN
8.2.
Accessibility
and
topologica!
transitivity
................... 88
8.3.
Stability of accessibility I: C1-genericity
................... 90
8.4.
Stability of accessibility II: particular results
............... 99
9.
The Pugh-Shub Ergodicity Theory
.............................. 107
10.
Stable Ergodicity
............................................... 112
10.1.
The Pugh -Shub Stable Ergodicity Theorem
.............. 112
10.2.
Frame flows
.............................................. 113
10.3.
Pathological foliations
.................................... 113
References
........................................................... 117
Index
................................................................ 121
|
| any_adam_object | 1 |
| author | Pesin, Yakov B. 1946- |
| author_GND | (DE-588)129370533 |
| author_facet | Pesin, Yakov B. 1946- |
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| author_sort | Pesin, Yakov B. 1946- |
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| ctrlnum | (OCoLC)56210818 (DE-599)BVBBV019392361 |
| dewey-full | 514.72 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 514 - Topology |
| dewey-raw | 514.72 |
| dewey-search | 514.72 |
| dewey-sort | 3514.72 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| indexdate | 2024-07-09T19:59:14Z |
| institution | BVB |
| isbn | 9783037190036 3037190035 |
| language | English |
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| series2 | Zurich lectures in advanced mathematics |
| spelling | Pesin, Yakov B. 1946- Verfasser (DE-588)129370533 aut Lectures on partial hyperbolicity and stable ergodicity Yakov B. Pesin Zürich European Mathematical Society 2004 VI, 122 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Zurich lectures in advanced mathematics Feuilletages (Mathématiques) Folheações (topologia diferencial) larpcal Fonctions exponentielles Sistemas dinâmicos larpcal Teoria ergodica larpcal Exponential functions Foliations (Mathematics) Ergodentheorie (DE-588)4015246-7 gnd rswk-swf Dynamisches System (DE-588)4013396-5 gnd rswk-swf Hyperbolisches System (DE-588)4191897-6 gnd rswk-swf Ergodentheorie (DE-588)4015246-7 s Hyperbolisches System (DE-588)4191897-6 s DE-604 Dynamisches System (DE-588)4013396-5 s Erscheint auch als elektronische Ausgabe Pesin, Yakov B. Lectures on partial hyperbolicity and stable ergodicity 978-3-03719-503-1 (DE-604)BV036752836 Digitalisierung UB Augsburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012855028&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Pesin, Yakov B. 1946- Lectures on partial hyperbolicity and stable ergodicity Feuilletages (Mathématiques) Folheações (topologia diferencial) larpcal Fonctions exponentielles Sistemas dinâmicos larpcal Teoria ergodica larpcal Exponential functions Foliations (Mathematics) Ergodentheorie (DE-588)4015246-7 gnd Dynamisches System (DE-588)4013396-5 gnd Hyperbolisches System (DE-588)4191897-6 gnd |
| subject_GND | (DE-588)4015246-7 (DE-588)4013396-5 (DE-588)4191897-6 |
| title | Lectures on partial hyperbolicity and stable ergodicity |
| title_auth | Lectures on partial hyperbolicity and stable ergodicity |
| title_exact_search | Lectures on partial hyperbolicity and stable ergodicity |
| title_full | Lectures on partial hyperbolicity and stable ergodicity Yakov B. Pesin |
| title_fullStr | Lectures on partial hyperbolicity and stable ergodicity Yakov B. Pesin |
| title_full_unstemmed | Lectures on partial hyperbolicity and stable ergodicity Yakov B. Pesin |
| title_short | Lectures on partial hyperbolicity and stable ergodicity |
| title_sort | lectures on partial hyperbolicity and stable ergodicity |
| topic | Feuilletages (Mathématiques) Folheações (topologia diferencial) larpcal Fonctions exponentielles Sistemas dinâmicos larpcal Teoria ergodica larpcal Exponential functions Foliations (Mathematics) Ergodentheorie (DE-588)4015246-7 gnd Dynamisches System (DE-588)4013396-5 gnd Hyperbolisches System (DE-588)4191897-6 gnd |
| topic_facet | Feuilletages (Mathématiques) Folheações (topologia diferencial) Fonctions exponentielles Sistemas dinâmicos Teoria ergodica Exponential functions Foliations (Mathematics) Ergodentheorie Dynamisches System Hyperbolisches System |
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