Dynamics of foliations, groups and pseudogroups:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Basel ; Boston ; Berlin
Birkhäuser
2004
|
| Series: | Monografie matematyczne
64 = new series |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis Klappentext |
| Item Description: | Literaturverz. S. 211 - 222 |
| Physical Description: | XI, 225 S. graph. Darst. 24 cm |
| ISBN: | 3764370912 |
Staff View
MARC
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| 245 | 1 | 0 | |a Dynamics of foliations, groups and pseudogroups |c Paweł Walczak |
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Record in the Search Index
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|---|---|
| adam_text | Contents
Preface
ix
1
Dynamical systems
1
1.1
Pseudogroups
.............................. 1
1.2
First examples
............................. 3
1.3
Foliations, laminations and holonomy
.................
б
1.4
Markov pseudogroups
......................... 15
1.5
Hyperbolic spaces and groups
..................... 20
2
Growth
33
2.1
Growth types
.............................. 34
2.2
Growth in groups
............................ 36
2.3
Orbit growth for pseudogroups
.................... 44
2.4
Expansion growth
........................... 51
3
Entropy
61
3.1
Entropy of classical systems
...................... 62
3.1.1
Topological entropy of a transformation
........... 62
3.1.2
Invariant measures
....................... 65
3.1.3
Measure-theoretic entropy
................... 66
3.1.4
Examples
............................ 68
3.15
Variational principle
...................... 70
3.2
Entropy of pseudogroups
........................ 73
3.3
Geometric entropy of foliations
.................... 76
3.4
Relating various entropies
....................... 79
3.5
Examples and constructions
...................... 84
3.5.1
Pullback
............................. 84
3.5.2
Gluing
.............................. 85
3.5.3
Turbulization
.......................... 86
3.6
Entropy and resiliency
......................... 89
viii Contents
4
Invariant
measures
97
4.1
Basic
definitions and facts
....................... 97
4.2
Transverse invariant measures and homology
............ 101
4.3
Measures and orbit growth
...................... 102
4.4
Transverse invariant measures in codimension
1........... 104
4.5
Vanishing entropy and invariant measures
.............. 106
4.6
Entropy, geodesic flow and invariant measures
........... 108
4.7
Harmonic measures
........................... 125
4.8
Patterson-Sullivan measures
...................... 142
5
Hausdorff dimension
155
5.1
Definitions and basic facts
....................... 155
5.2
Julia sets
................................ 161
5.3
Dimension in foliated manifolds
.................... 166
5.4
Dimension of a hyperbolic boundary
................. 176
5.5
Dimension of a limit set
........................ 179
6
Varia
183
6.1
Complexity growth
........................... 183
6.2
Expansive systems
........................... 187
6.3
Pseudo-orbits and pseudoleaves
.................... 191
6.4
Generic leaves
.............................. 201
Bibliography
211
Index
223
Paweł Walczak
Dynamics of
Foliations,
Groups and Pseudogroups
Foliations, groups and pseudogroups are objects which are closely related via the
notion of holonomy. In the
1980s
they became considered as general dynamical
systems. This book deals with their dynamics. Since dynamics is a very extensive
term, we focus on some of its aspects only. Roughly speaking, we concentrate
on notions and results related to different ways of measuring complexity of the
systems under consideration. More precisely, we deal with different types of
growth, entropies and dimensions of limiting objects. Invented in the
1980s
(by
E. Ghys, R.
Langevin
and the author) geometric entropy of a foliation is the
principal object of interest among all of them.
Throughout the book, the reader will find a good number of inspiring problems
related to the topics covered.
ISBN
3-7643-7091-2
783764 370916
www.birkhauser.ch
|
| any_adam_object | 1 |
| author | Walczak, Paweł 1948- |
| author_GND | (DE-588)1019417374 |
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| author_role | aut |
| author_sort | Walczak, Paweł 1948- |
| author_variant | p w pw |
| building | Verbundindex |
| bvnumber | BV036770160 |
| classification_rvk | SK 350 |
| ctrlnum | (OCoLC)249321306 (DE-599)DNB970127200 |
| 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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| id | DE-604.BV036770160 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T22:47:42Z |
| institution | BVB |
| isbn | 3764370912 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-020687037 |
| oclc_num | 249321306 |
| open_access_boolean | |
| owner | DE-703 |
| owner_facet | DE-703 |
| physical | XI, 225 S. graph. Darst. 24 cm |
| publishDate | 2004 |
| publishDateSearch | 2004 |
| publishDateSort | 2004 |
| publisher | Birkhäuser |
| record_format | marc |
| series | Monografie matematyczne |
| series2 | Monografie matematyczne |
| spelling | Walczak, Paweł 1948- Verfasser (DE-588)1019417374 aut Dynamics of foliations, groups and pseudogroups Paweł Walczak Basel ; Boston ; Berlin Birkhäuser 2004 XI, 225 S. graph. Darst. 24 cm txt rdacontent n rdamedia nc rdacarrier Monografie matematyczne 64 = new series Literaturverz. S. 211 - 222 Blätterung (DE-588)4007006-2 gnd rswk-swf Pseudogruppe (DE-588)4176130-3 gnd rswk-swf Topologische Dynamik (DE-588)4253345-4 gnd rswk-swf Transformationsgruppe (DE-588)4127386-2 gnd rswk-swf Topologische Dynamik (DE-588)4253345-4 s Blätterung (DE-588)4007006-2 s Transformationsgruppe (DE-588)4127386-2 s Pseudogruppe (DE-588)4176130-3 s DE-604 Monografie matematyczne 64 = new series (DE-604)BV000003532 64 Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020687037&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020687037&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Walczak, Paweł 1948- Dynamics of foliations, groups and pseudogroups Monografie matematyczne Blätterung (DE-588)4007006-2 gnd Pseudogruppe (DE-588)4176130-3 gnd Topologische Dynamik (DE-588)4253345-4 gnd Transformationsgruppe (DE-588)4127386-2 gnd |
| subject_GND | (DE-588)4007006-2 (DE-588)4176130-3 (DE-588)4253345-4 (DE-588)4127386-2 |
| title | Dynamics of foliations, groups and pseudogroups |
| title_auth | Dynamics of foliations, groups and pseudogroups |
| title_exact_search | Dynamics of foliations, groups and pseudogroups |
| title_full | Dynamics of foliations, groups and pseudogroups Paweł Walczak |
| title_fullStr | Dynamics of foliations, groups and pseudogroups Paweł Walczak |
| title_full_unstemmed | Dynamics of foliations, groups and pseudogroups Paweł Walczak |
| title_short | Dynamics of foliations, groups and pseudogroups |
| title_sort | dynamics of foliations groups and pseudogroups |
| topic | Blätterung (DE-588)4007006-2 gnd Pseudogruppe (DE-588)4176130-3 gnd Topologische Dynamik (DE-588)4253345-4 gnd Transformationsgruppe (DE-588)4127386-2 gnd |
| topic_facet | Blätterung Pseudogruppe Topologische Dynamik Transformationsgruppe |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020687037&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020687037&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000003532 |
| work_keys_str_mv | AT walczakpaweł dynamicsoffoliationsgroupsandpseudogroups |