Substitution dynamical systems - spectral analysis:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | German |
| Published: |
Berlin u.a.
Springer
1987
|
| Series: | Lecture notes in mathematics
1294 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIII, 240 S. |
| ISBN: | 3540186921 0387186921 |
Staff View
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| 245 | 1 | 0 | |a Substitution dynamical systems - spectral analysis |
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Record in the Search Index
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|---|---|
| adam_text | CONTENTS
PREFACE
INTRODUCTION
CHAPTER I THE ALGEBRA M(T) 1
1. Basic definitions 1
2. Generalized characters 4
3. Generalized Riesz products 7
4. Idempotents in A and decompositions of M(T) .. 11
5. Dirichlet measures 12
CHAPTER II SPECTRAL THEORY OF UNITARY OPERATORS 15
1. Representation theorem of unitary operators .... 15
2. Simple spectrum 20
3. Spectral decomposition theorems 22
4. Eigenvalues and discrete spectrum 30
CHAPTER III SPECTRAL THEORY OF DYNAMICAL SYSTEMS 35
1. Ergodicity 35
2. Ergodlc theorems 38
3. Purity laws and D ergodicity 40
4. Ergodic discrete systems 44
5. Mixing properties 47
6. Example 55
CHAPTER IV DYNAMICAL SYSTEMS ASSOCIATED TO SEQUENCES ... 60
1. Topological dynamical systems 60
2. Systems associated to sequences taking values in a
finite set 69
3. Spectral properties of sequences 73
CHAPTER V DYNAMICAL SYSTEMS ARISING FROM SUBSTITUTIONS . 87
1. Definitions and notations 87
2. Minimality of the topological system 89
XII
3. C matrix. Positive matrices
4. Unique ergodicity of the system (X(c),T) 95
5. Matrices M^ 1°°
6. Complexity and topological entropy 104
7. Recognizability property 108
CHAPTER VI EIGENVALUES OF SUBSTITUTION DYNAMICAL SYSTEM.
1. £(X) induced transformation 11°
2. Eigenvalues of an admissible substitution of
constant length 116
3. Eigenvalues of an admissible substitution of
non constant length 125
4. Discrete substitution of constant length 132
5. Open problems 136
CHAPTER VII MATRICES OF MEASURES 144
1. Reduction to the matrix E 144
2. Matrices of measures 151
3. Characters on a matrix of measures 156
CHAPTER VIII MATRIX RIESZ PRODUCTS 160
1. £ as matrix Riesz product 160
2. Examples of maximal spectral type 164
3. Commutative automata 169
CHAPTER IX BIJECTIVE AUTOMATA OR SUBSTITUTIONS 174
1. Structure of bijective substitution systems ... 175
2. Spectral study of bijective substitutions 180
CHAPTER X MAXIMAL SPECTRAL TYPE OF GENERAL AUTOMATA .. 19°
1. Colcidence matrix 190
2. Projection operator P 195
3. Matrix of correlation measures Z 200
4. Main theorem 205
CHAPTER XI SPECTRAL MULTIPLICITY OF GENERAL AUTOMATA ... 210
1. The convex set K 210
2. Spectral multiplicity of substitutions of cons¬
tant length 216
3. More about spectral multiplicity 224
XIII
APPENDIX COMPACT AUTOMATA 225
BIBLIOGRAPHY 231
INDEX 239
|
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| author_sort | Queffélec, Martine |
| author_variant | m q mq |
| building | Verbundindex |
| bvnumber | BV000769279 |
| classification_rvk | SI 850 |
| classification_tum | MAT 358f MAT 344f |
| ctrlnum | (OCoLC)246275041 (DE-599)BVBBV000769279 |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV000769279 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:19:09Z |
| institution | BVB |
| isbn | 3540186921 0387186921 |
| language | German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-000481488 |
| oclc_num | 246275041 |
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| physical | XIII, 240 S. |
| publishDate | 1987 |
| publishDateSearch | 1987 |
| publishDateSort | 1987 |
| publisher | Springer |
| record_format | marc |
| series | Lecture notes in mathematics |
| series2 | Lecture notes in mathematics |
| spelling | Queffélec, Martine Verfasser (DE-588)111580048 aut Substitution dynamical systems - spectral analysis Berlin u.a. Springer 1987 XIII, 240 S. txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 1294 Spektraltheorie (DE-588)4116561-5 gnd rswk-swf Substitution (DE-588)4183925-0 gnd rswk-swf Dynamisches System (DE-588)4013396-5 gnd rswk-swf Dynamisches System (DE-588)4013396-5 s Spektraltheorie (DE-588)4116561-5 s DE-604 Substitution (DE-588)4183925-0 s Lecture notes in mathematics 1294 (DE-604)BV000676446 1294 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000481488&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Queffélec, Martine Substitution dynamical systems - spectral analysis Lecture notes in mathematics Spektraltheorie (DE-588)4116561-5 gnd Substitution (DE-588)4183925-0 gnd Dynamisches System (DE-588)4013396-5 gnd |
| subject_GND | (DE-588)4116561-5 (DE-588)4183925-0 (DE-588)4013396-5 |
| title | Substitution dynamical systems - spectral analysis |
| title_auth | Substitution dynamical systems - spectral analysis |
| title_exact_search | Substitution dynamical systems - spectral analysis |
| title_full | Substitution dynamical systems - spectral analysis |
| title_fullStr | Substitution dynamical systems - spectral analysis |
| title_full_unstemmed | Substitution dynamical systems - spectral analysis |
| title_short | Substitution dynamical systems - spectral analysis |
| title_sort | substitution dynamical systems spectral analysis |
| topic | Spektraltheorie (DE-588)4116561-5 gnd Substitution (DE-588)4183925-0 gnd Dynamisches System (DE-588)4013396-5 gnd |
| topic_facet | Spektraltheorie Substitution Dynamisches System |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000481488&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000676446 |
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