Advanced Search
Article Contents
Article Contents

Realizing subexponential entropy growth rates by cutting and stacking

Abstract Related Papers Cited by
  • We show that for any concave positive function $f$ defined on $[0,\infty)$ with $\lim_{x\rightarrow\infty}f(x)/x=0$ there exists a rank one system $(X_f,T_f)$ such that $\limsup_{n\rightarrow\infty} H(\alpha_0^{n-1})/f(n)\ge 1$ for all nontrivial partitions $\alpha$ of $X_f$ into two sets and that there is one partition $\alpha$ of $X_f$ into two sets for which the limit superior of $H(\alpha_0^{n-1})/f(n)$ is equal to one whenever the condition $\lim_{x\rightarrow\infty}\ln x/f(x)=0$ is satisfied. Furthermore, for each system $(X_f,T_f)$ we also identify the minimal entropy growth rate in the limit inferior.
    Mathematics Subject Classification: Primary: 28D20; Secondary: 27A99.


    \begin{equation} \\ \end{equation}
  • [1]

    F. Blume, An entropy estimate for infinite interval exchange transformations, Mathematische Zeitschrift, 272 (2012), 17-29.doi: 10.1007/s00209-011-0919-2.


    F. Blume, Minimal rates of entropy convergence for completely ergodic systems, Israel Journal of Mathematics, 108 (1998), 1-12.doi: 10.1007/BF02783038.


    F. Blume, Minimal rates of entropy convergence for rank one systems, Discrete and Continuous Dynamical Systems, 6 (2000), 773-796.doi: 10.3934/dcds.2000.6.773.


    F. Blume, On the relation between entropy and the average complexity of trajectories in dynamical systems, Computational Complexity, 9 (2000), 146-155.doi: 10.1007/PL00001604.


    F. Blume, On the relation between entropy convergence rates and Baire category, Mathematische Zeitschrift, 271 (2012), 723-750.doi: 10.1007/s00209-011-0887-6.


    F. Blume, Possible rates of entropy convergence, Ergodic Theory and Dynamical Systems, 17 (1997), 45-70.doi: 10.1017/S0143385797069733.


    F. Blume, The Rate of Entropy Convergence, Doctoral Dissertation, University of North Carolina at Chapel Hill, 1995.


    A. Katok and J.-P. Thouvenot, Slow entropy type invariants and smooth realization of commuting measure-preserving transformations, Annales de l'Institut Henri Poincare (B) Probability and Statistics, 33 (1997), 323-338.doi: 10.1016/S0246-0203(97)80094-5.


    W. Parry, Entropy and Generators in Ergodic Theory, Benjamin, New York, 1969.


    K. E. Petersen, Ergodic Theory, Cambridge University Press, New York, 1983.doi: 10.1017/CBO9780511608728.

  • 加载中

Article Metrics

HTML views() PDF downloads(226) Cited by(0)

Access History

Other Articles By Authors



    DownLoad:  Full-Size Img  PowerPoint