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Lowering topological entropy over subsets
| Content Provider | Scilit |
|---|---|
| Author | Huang, Wen Ye, Xiangdong Zhang, Guohua |
| Copyright Year | 2009 |
| Description | Let (X,T) be a topological dynamical system (TDS), and h(T,K) the topological entropy of a subset K of X. (X,T) is lowerable if for each 0≤h≤h(T,X) there is a non-empty compact subset with entropy h; it is hereditarily lowerable if each non-empty compact subset is lowerable; it is hereditarily uniformly lowerable if for each non-empty compact subset K and each 0≤h≤h(T,K) there is a non-empty compact subset $K_{h}$⊆K with $h(T,K_{h}$)=h and $K_{h}$ has at most one limit point. It is shown that each TDS with finite entropy is lowerable, and that a TDS (X,T) is hereditarily uniformly lowerable if and only if it is asymptotically h-expansive. |
| Related Links | http://arxiv.org/pdf/0811.4230 https://www.cambridge.org/core/services/aop-cambridge-core/content/view/7909FD29A37F98851A93CEBA6D66C264/S0143385709000066a.pdf/div-class-title-lowering-topological-entropy-over-subsets-div.pdf |
| Ending Page | 209 |
| Page Count | 29 |
| Starting Page | 181 |
| ISSN | 01433857 |
| e-ISSN | 14694417 |
| DOI | 10.1017/s0143385709000066 |
| Journal | Ergodic Theory and Dynamical Systems |
| Issue Number | 1 |
| Volume Number | 30 |
| Language | English |
| Publisher | Cambridge University Press (CUP) |
| Publisher Date | 2010-02-01 |
| Access Restriction | Open |
| Subject Keyword | Ergodic Theory and Dynamical Systems Topological Entropy Subset with Entropy |
| Content Type | Text |
| Resource Type | Article |
| Subject | Applied Mathematics |
