Some Notes on Topological Entropy of Subsets on Compact Uniform Spaces

• Zhongxuan Yang ^[1] ; Xiaojun Huang ^[1]
  1. [1] Chongqing University

     Chongqing University

     China

     
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 24, Nº 2, 2025
• Idioma: inglés
• Enlaces
  • Texto completo
• Resumen

  • In this manuscript, we aim to investigate the topological entropy defined on compact uniform spaces. First, we introduce the notions of measure-theoretic entropy and topological entropy of subsets on compact uniform spaces. Subsequently, we obtain a variational principle for topological entropy of subsets on compact uniform spaces.

• Referencias bibliográficas
  • 1. Adler, R.L., Konheim, A.G., McAndrew, M.H.: Topological entropy. Trans. American Math. Soc. 114(2), 309–319 (1965)
  • 2. Bowen, R.: Entropy for group endomorphisms and homogeneous spaces. Trans. American Math. Soc. 153, 401–414 (1971)
  • 3. Bowen, R.: Topological entropy for noncompact sets. Trans. American Math. Soc. 184, 125–136 (1973)
  • 4. Ceccherini-Silberstein, T., Coornaert, M.: Expansive actions with specification on uniform spaces, topological entropy, and the myhill...
  • 5. Dinaburg, E.I.: On the relations among various entropy characteristics of dynamical systems. Math. USSR-Izvestiya 5(2), 337 (1971)
  • 6. Feng, D.-J., Huang, W.: Variational principles for topological entropies of subsets. J. Funct. Anal. 263(8), 2228–2254 (2012)
  • 7. Hood, B.: Topological entropy and uniform spaces. J. London Math. Soc. 2(4), 633–641 (1974)
  • 8. Huang, X., Li, Z., Zhou, Y.: A variational principle of topological pressure on subsets for amenable group actions. Discrete & Continuous...
  • 9. James, I. M.: Topologies and uniformities. Springer Science & Business Media, (2013)
  • 10. Kelley, J. L.: General topology. Courier Dover Publications, (2017)
  • 11. Kolmogorov, A. N.: A new metric invariant of transient dynamical systems and automorphisms in lebesgue spaces. In Doklady Akademii Nauk,...
  • 12. Mattila, P.: Geometry of sets and measures in Euclidean spaces: fractals and rectifiability. Number 44. Cambridge university press, (1999)
  • 13. Nazarian Sarkooh, J.: Variational principle for topological pressure on subsets of non-autonomous dynamical systems. Bulletin Malaysian...
  • 14. Pesin, Y. B.: Dimension theory in dynamical systems: contemporary views and applications. University of Chicago Press, (2008)
  • 15. Salman, M., Wu, X., Das, R.: Sensitivity of nonautonomous dynamical systems on uniform spaces. Int. . Bifurcat. Chaos 31(01), 2150017...
  • 16. Sarkooh, J.N.: Variational principle for neutralized bowen topological entropy on subsets of free semigroup actions. Proc. -Math. Sci....
  • 17. Shao, H.: Topological entropy of nonautonomous dynamical systems on uniform spaces. J. Differ. Equ. 365, 100–126 (2023)
  • 18. Walters, P.: An introduction to ergodic theory. Springer-Verlag, (1982)
  • 19. Weil, A.: Sur les espaces à structure uniforme et sur la topologie générale. (No Title), (1938)
  • 20. Xiao, Q., Ma, D.: Variational principle of topological pressure of free semigroup actions for subsets. Qual. Theor. Dyn. Syst. 21(4),...
  • 21. Xu, L., Zhou, X.: Variational principles for entropies of nonautonomous dynamical systems. J. Dyn. Differ. Equ. 30, 1053–1062 (2018)
  • 22. Yan, K., Zeng, F.: Topological entropy, pseudo-orbits and uniform spaces. Topol. Appl. 210, 168–182 (2016)
  • 23. Yang, R., Chen, E., Zhou, X.: Bowen’s equations for upper metric mean dimension with potential. Nonlinearity 35(9), 4905 (2022)
  • 24. Zheng, D., Chen, E.: Bowen entropy for actions of amenable groups. Israel J. Math. 212, 895–911 (2016)
  • 25. Zhong, X.-F., Chen, Z.-J.: Variational principles for topological pressures on subsets. Nonlinearity 36(2), 1168–1197 (2023)