Ergodic theory and differentiable dynamics:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin ; Heidelberg ; New York ; London ; Paris ; Tokyo
Springer
1987
|
| Schriftenreihe: | Ergebnisse der Mathematik und ihrer Grenzgebiete
8 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturverz. S. 305 - 308 |
| Beschreibung: | XII, 317 S. 32 Ill. |
| ISBN: | 3540152784 0387152784 |
Internformat
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| 100 | 1 | |a Mañé, Ricardo |e Verfasser |4 aut | |
| 240 | 1 | 0 | |a Introduçao à teoria ergódica |
| 245 | 1 | 0 | |a Ergodic theory and differentiable dynamics |c Ricardo Mañé. Transl. from the Portuguese by Silvio Levy |
| 264 | 1 | |a Berlin ; Heidelberg ; New York ; London ; Paris ; Tokyo |b Springer |c 1987 | |
| 300 | |a XII, 317 S. |b 32 Ill. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Ergebnisse der Mathematik und ihrer Grenzgebiete : Folge 3 |v 8 | |
| 500 | |a Literaturverz. S. 305 - 308 | ||
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| 650 | 0 | 7 | |a Ergodentheorie |0 (DE-588)4015246-7 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Ergodentheorie |0 (DE-588)4015246-7 |D s |
| 689 | 0 | 1 | |a Differenzierbares dynamisches System |0 (DE-588)4137931-7 |D s |
| 689 | 0 | |5 DE-604 | |
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| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-019121344 | |
Datensatz im Suchindex
| _version_ | 1807321378029830144 |
|---|---|
| adam_text |
TABLE
OF
CONTENTS
CHAPTER
0.
MEASURE
THEORY
.
1
1.
MEASURES
.
1
2.
MEASURABLE
MAPS
.
3
3.
INTEGRABLE
FUNCTIONS
.
3
4.
DIFFERENTIATION
AND
INTEGRATION
.
6
5.
PARTITIONS
AND
DERIVATIVES
.
7
CHAPTER
I.
MEASURE-PRESERVING
MAPS
.
15
1.
INTRODUCTION
.
15
2.
THE
POINCARE
RECURRENCE
THEOREM
.
27
3.
VOLUME-PRESERVING
DIFFEOMORPHISMS
AND
FLOWS
.
32
4.
FIRST
INTEGRALS
.
37
5.
HAMILTONIANS
.
39
6.
CONTINUED
FRACTIONS
.
42
7.
TOPOLOGICAL
GROUPS,
LIE
GROUPS,
HAAR
MEASURE
.
45
8.
INVARIANT
MEASURES
.
52
9.
UNIQUELY
ERGODIC
MAPS
.
58
10.
SHIFTS:
THE
PROBABILISTIC
VIEWPOINT
.
61
11.
SHIFTS:
THE
TOPOLOGICAL
VIEWPOINT
.
67
12.
EQUIVALENT
MAPS
.
77
CHAPTER
II.
ERGODICITY
.
89
1.
BIRKHOFF
'
S
THEOREM
.
89
2.
ERGODICITY
.
100
3.
ERGODICITY
OF
HOMOMORPHISMS
AND
TRANSLATIONS
OF
THE
TORUS
.
106
4.
MORE
EXAMPLES
OF
ERGODIC
MAPS
.
109
5.
THE
THEOREM
OF
KOLMOGOROV-ARNOLD-MOSER
.
125
6.
ERGODIC
DECOMPOSITION
OF
INVARIANT
MEASURES
.
127
7.
FURSTENBERG
'
S
EXAMPLE
.
134
8.
MIXING
AUTOMORPHISMS
AND
LEBESGUE
AUTOMORPHISMS
.
141
9.
SPECTRAL
THEORY
.
148
10.
GAUSSIAN
SHIFTS
.
151
11.
KOLMOGOROV
AUTOMORPHISMS
.
157
12.
MIXING
AND
ERGODIC
MARKOV
SHIFTS
.
161
XII
TABLE
OF
CONTENTS
CHAPTER
III.
EXPANDING
MAPS
AND
ANOSOV
DIFFEOMORPHISMS
.
166
1.
EXPANDING
MAPS
.
166
2.
ANOSOV
DIFFEOMORPHISMS
.
178
3.
ABSOLUTE
CONTINUITY
OF
THE
STABLE
FOLIATION
.
189
CHAPTER
IV.
ENTROPY
.
207
1.
INTRODUCTION
.
207
2.
PROOF
OF
THE
SHANNON-MCMILLAN-BREIMAN
THEOREM
.
212
3.
ENTROPY
.
214
4.
THE
KOLMOGOROV-SINAI
THEOREM
.
218
5.
ENTROPY
OF
EXPANDING
MAPS
.
227
6.
THE
PARRY
MEASURE
.
231
7.
TOPOLOGICAL
ENTROPY
.
236
8.
THE
VARIATIONAL
PROPERTY
OF
ENTROPY
.
244
9.
HYPERBOLIC
HOMEOMORPHISMS
.
251
10.
LYAPUNOV
EXPONENTS.
THE THEOREMS
OF
OSELEDEC
AND
PESIN
.
263
11.
PROOF
OF
OSELEDEC
'
S
THEOREM
.
267
12.
PROOF
OF
RUELLE
'
S
INEQUALITY
.
281
13.
PROOF
OF
PESIN
'
S
FORMULA
.
285
14.
ENTROPY
OF
ANOSOV
DIFFEOMORPHISMS
.
293
15.
HYPERBOLIC
MEASURES.
KATOK
'
S
THEOREM
.
296
16.
THE
BRIN-KATOK
LOCAL
ENTROPY
FORMULA
.
298
BIBLIOGRAPHY
.
305
NOTATION
INDEX
.
309
SUBJECT
INDEX
.
311 |
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| author | Mañé, Ricardo |
| author_facet | Mañé, Ricardo |
| author_role | aut |
| author_sort | Mañé, Ricardo |
| author_variant | r m rm |
| building | Verbundindex |
| bvnumber | BV025874136 |
| classification_rvk | SK 430 SK 810 |
| ctrlnum | (OCoLC)246406195 (DE-599)BVBBV025874136 |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV025874136 |
| illustrated | Illustrated |
| indexdate | 2024-08-14T00:39:39Z |
| institution | BVB |
| isbn | 3540152784 0387152784 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-019121344 |
| oclc_num | 246406195 |
| open_access_boolean | |
| owner | DE-11 |
| owner_facet | DE-11 |
| physical | XII, 317 S. 32 Ill. |
| publishDate | 1987 |
| publishDateSearch | 1987 |
| publishDateSort | 1987 |
| publisher | Springer |
| record_format | marc |
| series | Ergebnisse der Mathematik und ihrer Grenzgebiete |
| series2 | Ergebnisse der Mathematik und ihrer Grenzgebiete : Folge 3 |
| spelling | Mañé, Ricardo Verfasser aut Introduçao à teoria ergódica Ergodic theory and differentiable dynamics Ricardo Mañé. Transl. from the Portuguese by Silvio Levy Berlin ; Heidelberg ; New York ; London ; Paris ; Tokyo Springer 1987 XII, 317 S. 32 Ill. txt rdacontent n rdamedia nc rdacarrier Ergebnisse der Mathematik und ihrer Grenzgebiete : Folge 3 8 Literaturverz. S. 305 - 308 Differenzierbares dynamisches System (DE-588)4137931-7 gnd rswk-swf Maßtheorie (DE-588)4074626-4 gnd rswk-swf Ergodentheorie (DE-588)4015246-7 gnd rswk-swf Ergodentheorie (DE-588)4015246-7 s Differenzierbares dynamisches System (DE-588)4137931-7 s DE-604 Maßtheorie (DE-588)4074626-4 s Ergebnisse der Mathematik und ihrer Grenzgebiete 8 (DE-604)BV000899194 8 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=019121344&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Mañé, Ricardo Ergodic theory and differentiable dynamics Ergebnisse der Mathematik und ihrer Grenzgebiete Differenzierbares dynamisches System (DE-588)4137931-7 gnd Maßtheorie (DE-588)4074626-4 gnd Ergodentheorie (DE-588)4015246-7 gnd |
| subject_GND | (DE-588)4137931-7 (DE-588)4074626-4 (DE-588)4015246-7 |
| title | Ergodic theory and differentiable dynamics |
| title_alt | Introduçao à teoria ergódica |
| title_auth | Ergodic theory and differentiable dynamics |
| title_exact_search | Ergodic theory and differentiable dynamics |
| title_full | Ergodic theory and differentiable dynamics Ricardo Mañé. Transl. from the Portuguese by Silvio Levy |
| title_fullStr | Ergodic theory and differentiable dynamics Ricardo Mañé. Transl. from the Portuguese by Silvio Levy |
| title_full_unstemmed | Ergodic theory and differentiable dynamics Ricardo Mañé. Transl. from the Portuguese by Silvio Levy |
| title_short | Ergodic theory and differentiable dynamics |
| title_sort | ergodic theory and differentiable dynamics |
| topic | Differenzierbares dynamisches System (DE-588)4137931-7 gnd Maßtheorie (DE-588)4074626-4 gnd Ergodentheorie (DE-588)4015246-7 gnd |
| topic_facet | Differenzierbares dynamisches System Maßtheorie Ergodentheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=019121344&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000899194 |
| work_keys_str_mv | AT manericardo introducaoateoriaergodica AT manericardo ergodictheoryanddifferentiabledynamics |