Reversibility in dynamics and group theory:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge
Cambridge Univ. Press
2015
|
| Edition: | 1. publ. |
| Series: | London Mathematical Society lecture note series
416 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Includes bibliographical references and indexes |
| Physical Description: | XII, 281 S. graph. Darst. |
| ISBN: | 9781107442887 |
Staff View
MARC
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| 245 | 1 | 0 | |a Reversibility in dynamics and group theory |c Anthony G. O'Farrell ; Ian Short |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Cambridge |b Cambridge Univ. Press |c 2015 | |
| 300 | |a XII, 281 S. |b graph. Darst. | ||
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| 490 | 1 | |a London Mathematical Society lecture note series |v 416 | |
| 500 | |a Includes bibliographical references and indexes | ||
| 650 | 4 | |a Conjugacy classes | |
| 650 | 4 | |a Group theory | |
| 650 | 4 | |a Automorphisms | |
| 650 | 4 | |a Dynamics | |
| 650 | 4 | |a Reverse mathematics | |
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Record in the Search Index
| _version_ | 1804153026687008768 |
|---|---|
| adam_text | : ix
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Contents
Preface
Origins
1.1 Origins in dynamical systems
1.2 Origins in finite group theory
1.3 Origins in hidden dynamics
1.4 The reversibility problem
Basic ideas
2.1 Reversibility
2.2 Reformulations
2.3 Signed groups
2.4 Whither next?
Finite groups
3.1 Reversers of finite order
3.2 Dihedral groups
3.3 Symmetric groups
3.4 Alternating groups
3.5 Group characters
3.6 Characters and reversible elements
3.7 Characters and strongly-reversible elements
3.8 Examples
3.9 Free groups
The classical groups
4.1 The classical groups
4.2 The general linear group
4.3 The orthogonal group
4.4 The unitary group
4.5 Summary
v
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Contents
Compact groups
5.1 Reversibility in compact groups
5.2 Compact Lie groups
5.3 The special unitary group
5.4 Comp act symplectic group s
5.5 The spinor groups
Isometry groups
6.1 Isometries of spherical, Euclidean, and hyperbolic space
6.2 Hyperbolic geometry in two and three dimensions
6.3 Euclidean isometries
6.4 Hyperbolic isometries
Groups of integer matrices
7.1 Conjugacy to rational canonical form
7.2 Integral quadratic forms
7.3 Conway’s topograph
7.4 Gauss’ method for definite forms
7.5 Elliptic elements of GL(2,Z)
7.6 Centralisers
7.7 Reversible elements
7.8 Second associated form
7.9 Gauss’ method for indefinite forms
7.10 Another way
7.11 Суchcally-reduced words
Real homeomorphisms
8.1 Involutions
8.2 Conjugacy
8.3 Reflectional and rotational symmetries
8.4 Reversible elements
8.5 Products of involutions and reversible elements
Circle homeomorphisms
9.1 Involutions
9.2 Conjugacy
9.3 Reversible elements
9.4 Strongly-reversible elements
9.5 Products of involutions
Formal power series
10.1 Power series structures
10.2 Elements of finite order
Contents
vii
10.3 Conjugacy 193
10.4 Centralisers 196
10.5 Products of involutions modulo V4 203
10.6 Strongly-reversible elements 204
10.7 Products of involutions 206
10.8 Reversible series 208
10.9 Reversers 210
10.10 Products of reversible senes 211
11 Real diffeomorphisms 216
11.1 Involutions 217
11.2 Fixed-pomt-free maps 218
11.3 Centralisers 220
11.4 Reversibility of order-preserving diffeomorphisms 223
11.5 Reversibility in the full diffeomorphism group 226
11.6 Products of involutions and reversible elements 230
12 Biholomorphic germs 234
12.1 Elements of finite order 235
12.2 Conjugacy 236
12.3 Ecalle-Voronin theory 237
12.4 Roots 242
12.5 Centralisers and flows 243
12.6 Reversible and strongly-reversible elements 245
12.7 The order of a reverser 247
12.8 Examples 248
References 261
List of frequently used symbols 275
Index of names ll !
Subject index 279
|
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| id | DE-604.BV042382826 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T01:20:04Z |
| institution | BVB |
| isbn | 9781107442887 |
| language | English |
| lccn | 014023512 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027818874 |
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| physical | XII, 281 S. graph. Darst. |
| publishDate | 2015 |
| publishDateSearch | 2015 |
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| publisher | Cambridge Univ. Press |
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| series | London Mathematical Society lecture note series |
| series2 | London Mathematical Society lecture note series |
| spelling | O'Farrell, Anthony G. Verfasser aut Reversibility in dynamics and group theory Anthony G. O'Farrell ; Ian Short 1. publ. Cambridge Cambridge Univ. Press 2015 XII, 281 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier London Mathematical Society lecture note series 416 Includes bibliographical references and indexes Conjugacy classes Group theory Automorphisms Dynamics Reverse mathematics Umkehrbarkeit (DE-588)4427661-8 gnd rswk-swf Dynamisches System (DE-588)4013396-5 gnd rswk-swf Gruppentheorie (DE-588)4072157-7 gnd rswk-swf Gruppentheorie (DE-588)4072157-7 s Dynamisches System (DE-588)4013396-5 s Umkehrbarkeit (DE-588)4427661-8 s DE-604 Short, Ian 1979- Verfasser (DE-588)1072192101 aut London Mathematical Society lecture note series 416 (DE-604)BV000000130 416 Digitalisierung UB Regensburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027818874&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | O'Farrell, Anthony G. Short, Ian 1979- Reversibility in dynamics and group theory London Mathematical Society lecture note series Conjugacy classes Group theory Automorphisms Dynamics Reverse mathematics Umkehrbarkeit (DE-588)4427661-8 gnd Dynamisches System (DE-588)4013396-5 gnd Gruppentheorie (DE-588)4072157-7 gnd |
| subject_GND | (DE-588)4427661-8 (DE-588)4013396-5 (DE-588)4072157-7 |
| title | Reversibility in dynamics and group theory |
| title_auth | Reversibility in dynamics and group theory |
| title_exact_search | Reversibility in dynamics and group theory |
| title_full | Reversibility in dynamics and group theory Anthony G. O'Farrell ; Ian Short |
| title_fullStr | Reversibility in dynamics and group theory Anthony G. O'Farrell ; Ian Short |
| title_full_unstemmed | Reversibility in dynamics and group theory Anthony G. O'Farrell ; Ian Short |
| title_short | Reversibility in dynamics and group theory |
| title_sort | reversibility in dynamics and group theory |
| topic | Conjugacy classes Group theory Automorphisms Dynamics Reverse mathematics Umkehrbarkeit (DE-588)4427661-8 gnd Dynamisches System (DE-588)4013396-5 gnd Gruppentheorie (DE-588)4072157-7 gnd |
| topic_facet | Conjugacy classes Group theory Automorphisms Dynamics Reverse mathematics Umkehrbarkeit Dynamisches System Gruppentheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027818874&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000000130 |
| work_keys_str_mv | AT ofarrellanthonyg reversibilityindynamicsandgrouptheory AT shortian reversibilityindynamicsandgrouptheory |