Self-similar groups:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, Rhode Island
American Mathematical Society
[2005]
|
| Series: | Mathematical surveys and monographs
Volume 117 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | xi, 231 Seiten Diagramme |
| ISBN: | 9780821838310 0821838318 |
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Record in the Search Index
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| adam_text | MATHEMATICAL SURVEYS AND MONOGRAPHS VOLUME 117 SELF-SIMILAR GROUPS
VOLODYMYR NEKRASHEVYCH AMERICAN MATHEMATICAL SOCIETY CONTENTS PREFACE
VII CHAPTER 1. BASIC DEFINITIONS AND EXAMPLES 1 1.1. ROOTED TREE X* AND
ITS BOUNDARY X 1 1.2. GROUPS ACTING ON ROOTED TREES 2 1.3. AUTOMATA 3
1.4. WREATH PRODUCTS 9 1.5. SELF-SIMILAR ACTIONS 10 1.6. THE GRIGORCHUK
GROUP 12 1.7. THE ADDING MACHINE AND SELF-SIMILAR ACTIONS OF Z * 16 1.8.
BRANCH GROUPS 17 1.9. OTHER EXAMPLES 21 1.10. BI-REVERSIBLE AUTOMATA AND
FREE GROUPS 23 CHAPTER 2. ALGEBRAIC THEORY 31 2.1. PERMUTATIONAL
BIMODULES 31 2.2. BASES OF A COVERING BIMODULE AND WREATH RECURSIONS 32
2.3. TENSOR PRODUCTS AND SELF-SIMILAR ACTIONS 33 2.4. THE LEFT G-SPACE
9JT W 36 2.5. VIRTUAL ENDOMORPHISMS 37 2.6. THE LINEAR RECURSION 40
2.7. INVARIANT SUBGROUPS AND THE KERNEL OF A SELF-SIMILAR ACTION 41 2.8.
RECURRENT ACTIONS 44 2.9. EXAMPLE: FREE ABELIAN GROUPS 46 2.10. RIGIDITY
50 2.11. CONTRACTING ACTIONS 57 2.12. FINITE-STATE ACTIONS OF Z * 62
2.13. DEFINING RELATIONS AND WORD PROBLEM 64 CHAPTER 3. LIMIT SPACES 71
3.1. INTRODUCTION 71 3.2. THE LIMIT G-SPACE X G 73 3.3. DIGIT TILES 78
3.4. AXIOMATIC DESCRIPTION OF XQ 82 3.5. CONNECTEDNESS OF XQ 91 3.6. THE
LIMIT SPACE J G 92 3.7. LIMIT SPACES OF SELF-SIMILAR SUBGROUPS 96 3.8.
THE LIMIT SPACE JG AS A HYPERBOLIC BOUNDARY 97 3.9. GROUPS OF BOUNDED
AUTOMATA 102 3.10. ONE-DIMENSIONAL SUBDIVISION RULES 110 VI CONTENTS
3.11. UNIQUENESS OF THE LIMIT SPACE 113 CHAPTER 4. ORBISPACES 117 4.1.
PSEUDOGROUPS AND ETALE GROUPOIDS 117 4.2. ORBISPACES 119 4.3. OPEN
SUB-ORBISPACES AND COVERINGS 122 4.4. COVERINGS AND SKEW-PRODUCTS 124
4.5. PARTIAL SELF-COVERINGS 127 4.6. THE LIMIT ORBISPACE J G 128 4.7.
PATHS IN AN ORBISPACE 131 CHAPTER 5. ITERATED MONODROMY GROUPS 137 5.1.
DEFINITION OF ITERATED MONODROMY GROUPS 137 5.2. STANDARD SELF-SIMILAR
ACTIONS OF IMG (P) ON X* 142 5.3. ITERATED MONODROMY GROUPS OF LIMIT
DYNAMICAL SYSTEMS 146 5.4. LENGTH STRUCTURES AND EXPANDING MAPS 148 5.5.
LIMIT SPACES OF ITERATED MONODROMY GROUPS 150 5.6. ITERATED MONODROMY
GROUP OF A PULL-BACK 154 5.7. THE LIMIT SOLENOID AND INVERSE LIMITS OF
SELF-COVERINGS 156 CHAPTER 6. EXAMPLES AND APPLICATIONS 161 6.1.
EXPANDING SELF-COVERINGS OF ORBIFOLDS 161 6.2. LIMIT SPACES OF FREE
ABELIAN GROUPS 165 6.3. EXAMPLES OF SELF-COVERINGS OF ORBIFOLDS 169 6.4.
RATIONAL FUNCTIONS 174 6.5. COMBINATORIAL EQUIVALENCE AND THURSTON S
THEOREM 176 6.6. TWISTED RABBIT QUESTION OF J. HUBBARD 179 6.7.
ABSTRACT KNEADING AUTOMATA 185 6.8. TOPOLOGICAL POLYNOMIALS AND CRITICAL
PORTRAITS 190 6.9. ITERATED MONODROMY GROUPS OF COMPLEX POLYNOMIALS 193
6.10. POLYNOMIALS FROM KNEADING AUTOMATA 196 6.11. QUADRATIC POLYNOMIALS
203 6.12. EXAMPLES OF ITERATED MONODROMY GROUPS OF POLYNOMIALS 208 6.13.
MATINGS 215 BIBLIOGRAPHY 223 INDEX 229
|
| adam_txt |
MATHEMATICAL SURVEYS AND MONOGRAPHS VOLUME 117 SELF-SIMILAR GROUPS
VOLODYMYR NEKRASHEVYCH AMERICAN MATHEMATICAL SOCIETY CONTENTS PREFACE
VII CHAPTER 1. BASIC DEFINITIONS AND EXAMPLES 1 1.1. ROOTED TREE X* AND
ITS BOUNDARY X" 1 1.2. GROUPS ACTING ON ROOTED TREES 2 1.3. AUTOMATA 3
1.4. WREATH PRODUCTS 9 1.5. SELF-SIMILAR ACTIONS 10 1.6. THE GRIGORCHUK
GROUP 12 1.7. THE ADDING MACHINE AND SELF-SIMILAR ACTIONS OF Z * 16 1.8.
BRANCH GROUPS 17 1.9. OTHER EXAMPLES 21 1.10. BI-REVERSIBLE AUTOMATA AND
FREE GROUPS 23 CHAPTER 2. ALGEBRAIC THEORY 31 2.1. PERMUTATIONAL
BIMODULES 31 2.2. BASES OF A COVERING BIMODULE AND WREATH RECURSIONS 32
2.3. TENSOR PRODUCTS AND SELF-SIMILAR ACTIONS 33 2.4. THE LEFT G-SPACE
9JT W 36 2.5. VIRTUAL ENDOMORPHISMS 37 2.6. THE LINEAR RECURSION 40
2.7. INVARIANT SUBGROUPS AND THE KERNEL OF A SELF-SIMILAR ACTION 41 2.8.
RECURRENT ACTIONS 44 2.9. EXAMPLE: FREE ABELIAN GROUPS 46 2.10. RIGIDITY
50 2.11. CONTRACTING ACTIONS 57 2.12. FINITE-STATE ACTIONS OF Z * ' 62
2.13. DEFINING RELATIONS AND WORD PROBLEM 64 CHAPTER 3. LIMIT SPACES 71
3.1. INTRODUCTION 71 3.2. THE LIMIT G-SPACE X G 73 3.3. DIGIT TILES 78
3.4. AXIOMATIC DESCRIPTION OF XQ 82 3.5. CONNECTEDNESS OF XQ 91 3.6. THE
LIMIT SPACE J G 92 3.7. LIMIT SPACES OF SELF-SIMILAR SUBGROUPS 96 3.8.
THE LIMIT SPACE JG AS A HYPERBOLIC BOUNDARY 97 3.9. GROUPS OF BOUNDED
AUTOMATA 102 3.10. ONE-DIMENSIONAL SUBDIVISION RULES 110 VI CONTENTS
3.11. UNIQUENESS OF THE LIMIT SPACE 113 CHAPTER 4. ORBISPACES 117 4.1.
PSEUDOGROUPS AND ETALE GROUPOIDS 117 4.2. ORBISPACES 119 4.3. OPEN
SUB-ORBISPACES AND COVERINGS 122 4.4. COVERINGS AND SKEW-PRODUCTS 124
4.5. PARTIAL SELF-COVERINGS 127 4.6. THE LIMIT ORBISPACE J G 128 4.7.
PATHS IN AN ORBISPACE 131 CHAPTER 5. ITERATED MONODROMY GROUPS 137 5.1.
DEFINITION OF ITERATED MONODROMY GROUPS 137 5.2. STANDARD SELF-SIMILAR
ACTIONS OF IMG (P) ON X* 142 5.3. ITERATED MONODROMY GROUPS OF LIMIT
DYNAMICAL SYSTEMS 146 5.4. LENGTH STRUCTURES AND EXPANDING MAPS 148 5.5.
LIMIT SPACES OF ITERATED MONODROMY GROUPS 150 5.6. ITERATED MONODROMY
GROUP OF A PULL-BACK 154 5.7. THE LIMIT SOLENOID AND INVERSE LIMITS OF
SELF-COVERINGS 156 CHAPTER 6. EXAMPLES AND APPLICATIONS 161 6.1.
EXPANDING SELF-COVERINGS OF ORBIFOLDS 161 6.2. LIMIT SPACES OF FREE
ABELIAN GROUPS 165 6.3. EXAMPLES OF SELF-COVERINGS OF ORBIFOLDS 169 6.4.
RATIONAL FUNCTIONS 174 6.5. COMBINATORIAL EQUIVALENCE AND THURSTON'S
THEOREM 176 6.6. "TWISTED RABBIT" QUESTION OF J. HUBBARD 179 6.7.
ABSTRACT KNEADING AUTOMATA 185 6.8. TOPOLOGICAL POLYNOMIALS AND CRITICAL
PORTRAITS 190 6.9. ITERATED MONODROMY GROUPS OF COMPLEX POLYNOMIALS 193
6.10. POLYNOMIALS FROM KNEADING AUTOMATA 196 6.11. QUADRATIC POLYNOMIALS
203 6.12. EXAMPLES OF ITERATED MONODROMY GROUPS OF POLYNOMIALS 208 6.13.
MATINGS 215 BIBLIOGRAPHY 223 INDEX 229 |
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| illustrated | Not Illustrated |
| index_date | 2024-07-02T18:55:10Z |
| indexdate | 2024-07-09T21:07:57Z |
| institution | BVB |
| isbn | 9780821838310 0821838318 |
| language | English |
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| physical | xi, 231 Seiten Diagramme |
| publishDate | 2005 |
| publishDateSearch | 2005 |
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| publisher | American Mathematical Society |
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| spelling | Nekrashevych, Volodymyr 1975- Verfasser (DE-588)173796109 aut Self-similar groups Volodymyr Nekrashevych Providence, Rhode Island American Mathematical Society [2005] © 2005 xi, 231 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier Mathematical surveys and monographs Volume 117 Dynamique symbolique Groupes, Théorie géométrique des Teoria geométrica dos grupos larpcal Geometric group theory Self-similar processes Symbolic dynamics Selbstähnlichkeit (DE-588)4286650-9 gnd rswk-swf Gruppe Mathematik (DE-588)4022379-6 gnd rswk-swf Gruppentheorie (DE-588)4072157-7 gnd rswk-swf Gruppentheorie (DE-588)4072157-7 s Gruppe Mathematik (DE-588)4022379-6 s Selbstähnlichkeit (DE-588)4286650-9 s DE-604 Erscheint auch als Online-Ausgabe 978-1-4704-1344-6 Mathematical surveys and monographs Volume 117 (DE-604)BV000018014 117 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016137358&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Nekrashevych, Volodymyr 1975- Self-similar groups Mathematical surveys and monographs Dynamique symbolique Groupes, Théorie géométrique des Teoria geométrica dos grupos larpcal Geometric group theory Self-similar processes Symbolic dynamics Selbstähnlichkeit (DE-588)4286650-9 gnd Gruppe Mathematik (DE-588)4022379-6 gnd Gruppentheorie (DE-588)4072157-7 gnd |
| subject_GND | (DE-588)4286650-9 (DE-588)4022379-6 (DE-588)4072157-7 |
| title | Self-similar groups |
| title_auth | Self-similar groups |
| title_exact_search | Self-similar groups |
| title_exact_search_txtP | Self-similar groups |
| title_full | Self-similar groups Volodymyr Nekrashevych |
| title_fullStr | Self-similar groups Volodymyr Nekrashevych |
| title_full_unstemmed | Self-similar groups Volodymyr Nekrashevych |
| title_short | Self-similar groups |
| title_sort | self similar groups |
| topic | Dynamique symbolique Groupes, Théorie géométrique des Teoria geométrica dos grupos larpcal Geometric group theory Self-similar processes Symbolic dynamics Selbstähnlichkeit (DE-588)4286650-9 gnd Gruppe Mathematik (DE-588)4022379-6 gnd Gruppentheorie (DE-588)4072157-7 gnd |
| topic_facet | Dynamique symbolique Groupes, Théorie géométrique des Teoria geométrica dos grupos Geometric group theory Self-similar processes Symbolic dynamics Selbstähnlichkeit Gruppe Mathematik Gruppentheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016137358&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000018014 |
| work_keys_str_mv | AT nekrashevychvolodymyr selfsimilargroups |