Preimage entropy dimension of topological dynamical systems

Preprint English OPEN
Liu, Lei; Zhou, Xiaomin; Zhou, Xiaoyao;
(2014)
  • Subject: Mathematics - Dynamical Systems | 54H20, 37B20
    arxiv: Mathematics::Dynamical Systems | Mathematics::Complex Variables | Mathematics::General Topology | Nonlinear Sciences::Cellular Automata and Lattice Gases

We propose a new definition of preimage entropy dimension for continuous maps on compact metric spaces, investigate fundamental properties of the preimage entropy dimension, and compare the preimage entropy dimension with the topological entropy dimension. The defined p... View more
  • References (27)
    27 references, page 1 of 3

    [1] R. Adler, A. Konheim and M. McAndrew, Topological entropy, Trans. Amer. Math. Soc. 114 (1965), 309-319.

    [2] L. Block and W. Coppel, Dynamics in One Dimension. Lecture Notes in Mathematics, 1513, Springer Verlag, Berlin, 1992.

    [3] R. Bowen, Topological entropy and axiom A, Proc. Symp. Pure Math, Amer. Math. Soc. 14 (1970), 23-42.

    [4] R. Bowen, Entropy for group endomorphisms and homogeneous spaces, Trans. Amer. Math. Soc. 153 (1971), 401-414.

    [5] R. Bowen and P. Walters, Expansive one-parameter flows, J. Differ. Equat. 12 (1972), 180-193.

    [6] M. Carvalho, Entropy dimension of dynamical systems, Port. Math. 54 (1997) 19-40.

    [7] W. Cheng and S. Newhouse, Preimage entropy, Ergod. Th. Dynam. Sys. 25 (2005), 1091-1113.

    [8] W. Cheng and B. Li, Zero entropy systems, J. Stat. Phys. 140 (2010), 1006-1021.

    [9] W. Cheng and B. Li, Topological pressure dimension, Chaos Solitons Fractals 53 (2013), 10-17.

    [10] I. Cornfeld, S. Fomin and Y. Sinai, Ergodic theory, Springer, Berlin, 1982.

  • Related Organizations (3)
  • Metrics
Share - Bookmark