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Slow Entropy for Noncompact Sets and Variational Principle |
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| Authors: | Depeng Kong Ercai Chen |
| Affiliation: | 1. School of Mathematical Sciences and Institute of Mathematics, Nanjing Normal University, Nanjing, 210023, People’s Republic of China 2. Center of Nonlinear Science, Nanjing University, Nanjing, 210093, People’s Republic of China |
| Abstract: | This paper defines and discusses the dimension notion of topological slow entropy of any subset for ({{mathbb {Z}}}^d-) actions. Also, the notion of measure-theoretic slow entropy for ({mathbb {Z}}^d-) actions is presented, which is modified from Brin and Katok (Geometric Dynamics, Springer, Berlin 1983). Relations between Bowen topological entropy Bowen (Trans Am Math, 184:125–136, 1973), and topological slow entropy are studied in this paper, and several examples of the topological slow entropy in a symbolic system are given. Specifically, a variational principle is proved. |
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