Variational Principle for Neutralized Bowen Topological Entropy

• Rui Yang ^[1] ; Ercai Chen ^[1] ; Xiaoyao Zhou ^[1]
  1. [1] Nanjing Normal University

     Nanjing Normal University

     China

     
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 23, Nº 4, 2024
• Idioma: inglés
• DOI: 10.1007/s12346-024-01029-5
• Enlaces
  • Texto completo
• Resumen

  • Ovadia and Rodriguez-Hertz defined neutralized Bowen open ball as Bn(x, e−n ) = {y ∈ X : d(T j x, T j y) < e−n , ∀0 ≤ j ≤ n − 1}.

    We introduce the notion of neutralized Bowen topological entropy of subsets by neutralized Bowen open ball, and establish variational principles for neutralized Bowen topological entropy of compact subsets in terms of neutralized Brin–Katok local entropy and neutralized Katok’s entropy

• Referencias bibliográficas
  • 1. Adler, R., Konheim, A., McAndrew, M.: Topological entropy. Trans. Am. Math. Soc. 114, 309–319 (1965)
  • 2. Bowen, R.: Entropy for group endomorphisms and homogeneous spaces. Trans. Am. Math. Soc. 153, 401–414 (1971)
  • 3. Bowen, R.: Topological entropy for noncompact sets. Trans. Am. Math. Soc. 184, 125–136 (1973)
  • 4. Brin, M., Katok, A.: On local entropy, Geometric dynamics (Rio de Janeiro). Lecture Notes in Mathematics, vol. 1007, pp. 30–38. Springer,...
  • 5. Dou, D., Fan, M., Qiu, H.: Topological entropy on subsets for fixed-point free flows. Discrete Contin. Dyn. Syst. 37, 6319–6331 (2017)
  • 6. Feng, D., Huang, W.: Variational principles for topological entropies of subsets. J. Funct. Anal. 263, 2228–2254 (2012)
  • 7. Huang, X., Li, Z., Zhou, Y.: A variational principle of topological pressure on subsets for amenable group actions. Discrete Contin. Dyn....
  • 8. Katok, A.: Lyapunov exponents, entropy and periodic orbits for diffeomorphisms. Publ. Math. Inst. Hautes Études Sci. 51, 137–173 (1980)
  • 9. Kenyon, R., Peres, Y.: Intersecting random translates of invariant Cantor sets. Invent. Math. 104, 601–629 (1991)
  • 10. Lindenstrauss, E., Tsukamoto, M.: From rate distortion theory to metric mean dimension: variational principle. IEEE Trans. Inform. Theory...
  • 11. Liu, L., Jiao, J., Zhou, X.: Unstable pressure of subsets for partially hyperbolic systems. Dyn. Syst. 37, 564–577 (2022)
  • 12. Mattila, P.: The Geometry of Sets and Measures in Euclidean Spaces. Cambridge University Press, Cambridge (1995)
  • 13. Ovadia, S., Rodriguez-Hertz, F.: Neutralized local entropy and dimension bounds for invariant measures. Int. Math. Res. Not. IMRN, , rnae047...
  • 14. Pesin, Y.B.: Dimension Theory in Dynamical Systems. University of Chicago Press, New York (1997)
  • 15. Tian, X., Wu, W.: Unstable entropies and dimension theory of partially hyperbolic systems. Nonlinearity 35, 658–680 (2022)
  • 16. Walters, P.: An Introduction to Ergodic Theory. Springer, Berlin (1982)
  • 17. Wang, T.: Variational relations for metric mean dimension and rate distortion dimension. Discrete Contin. Dyn. Syst. 27, 4593–4608 (2021)
  • 18. Xiao, Q., Ma, D.: Variational principle of topological pressure of free semigroup actions for subsets. Qual. Theory Dyn. Syst. 21, 18...
  • 19. Xu, L., Zhou, X.: Variational principles for entropies of nonautonomous dynamical systems. J. Dyn. Differ. Equ. 30, 1053–1062 (2018)
  • 20. Zheng, D., Chen, E.: Bowen entropy for actions of amenable groups. Israel J. Math. 212, 895–911 (2016)
  • 21. Zhong, X., Chen, Z.: Variational principle for topological pressure on subsets of free semigroup actions. Acta Math. Sin. (Engl. Ser.)...
  • 22. Yang, R., Chen, E., Zhou, X.: Bowen’s equations for upper metric mean dimension with potential. Nonlinearity 35, 4905–4938 (2022)