eBook ISBN: | 978-1-4704-0258-7 |
Product Code: | MEMO/140/667.E |
List Price: | $60.00 |
MAA Member Price: | $54.00 |
AMS Member Price: | $36.00 |
eBook ISBN: | 978-1-4704-0258-7 |
Product Code: | MEMO/140/667.E |
List Price: | $60.00 |
MAA Member Price: | $54.00 |
AMS Member Price: | $36.00 |
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Book DetailsMemoirs of the American Mathematical SocietyVolume: 140; 1999; 197 ppMSC: Primary 54; 58; 34
Abstract
A simplicial dynamical system is a simplicial map \(g:K^* \rightarrow K\) where \(K\) is a finite simplicial complex triangulating a compact polyhedron \(X\) and \(K^*\) is a proper subdivision of \(K\), e.g. the barycentric or any further subdivision. The dynamics of the associated piecewise linear map \(g: X X\) can be analyzed by using certain naturally related subshifts of finite type. Any continuous map on \(X\) can be \(C^0\) approximated by such systems. Other examples yield interesting subshift constructions.
ReadershipGraduate students and research mathematicians working in topological dynamics.
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Table of Contents
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Chapters
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1. Chain recurrence and basic sets
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2. Simplicial maps and their local inverses
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3. The shift factor maps for a simplicial dynamical system
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4. Recurrence and basic set images
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5. Invariant measures
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6. Generalized simplicial dynamical systems
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7. Examples
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8. PL roundoffs of a continuous map
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9. Nondegenerate maps on manifolds
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10. Appendix: Stellar and lunar subdivisions
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11. Appendix: Hyperbolicity for relations
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Abstract
A simplicial dynamical system is a simplicial map \(g:K^* \rightarrow K\) where \(K\) is a finite simplicial complex triangulating a compact polyhedron \(X\) and \(K^*\) is a proper subdivision of \(K\), e.g. the barycentric or any further subdivision. The dynamics of the associated piecewise linear map \(g: X X\) can be analyzed by using certain naturally related subshifts of finite type. Any continuous map on \(X\) can be \(C^0\) approximated by such systems. Other examples yield interesting subshift constructions.
Graduate students and research mathematicians working in topological dynamics.
-
Chapters
-
1. Chain recurrence and basic sets
-
2. Simplicial maps and their local inverses
-
3. The shift factor maps for a simplicial dynamical system
-
4. Recurrence and basic set images
-
5. Invariant measures
-
6. Generalized simplicial dynamical systems
-
7. Examples
-
8. PL roundoffs of a continuous map
-
9. Nondegenerate maps on manifolds
-
10. Appendix: Stellar and lunar subdivisions
-
11. Appendix: Hyperbolicity for relations