α-estimation BS-Packing Dimension and Bowen’s Equation

• Fei Gao ^[1] ; Ercai Chen ^[1] ; Yunxiang Xie ^[1]
  1. [1] Nanjing Normal University

     Nanjing Normal University

     China

     
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 25, Nº 2, 2026
• Idioma: inglés
• Enlaces
  • Texto completo
• Resumen

  • Based on the α-metric dα n (x, y) = max0≤i

• Referencias bibliográficas
  • 1. Adler, R., Konheim, A., McAndrew, M.: Topological entropy. Trans. Amer. Math. Soc. 114, 309–319 (1965)
  • 2. Barreira, L., Schmeling, J.: Sets of “non-typical” points have full topological entropy and full Hausdorff dimension. Israel J. Math. 116,...
  • 3. Bowen, R.: Topological entropy for noncompact sets. Trans. Amer. Math. Soc. 184, 125–136 (1973)
  • 4. Bowen, R.:Hausdorff dimension of quasicircles. Inst. Hautes Études Sci. Publ.Math. 50, 11–25 (1979)
  • 5. Brin, M., Katok, A.: On local entropy, Geometric dynamics (Rio de Janeiro, 1981), 30-38, Lecture Notes in Math., 1007, Springer, Berlin
  • 6. Chen, E., Xiong, J.: Dimension and measure theoretic entropy of a subshift in symbolic space. Chinese Sci. Bull. 42, 1193–1196 (1997)
  • 7. Ding, Z., Yang, R., Zhou, X.: α-BS dimension on subsets. Banach J. Math. Anal. 20, (2026). https:// doi.org/10.1007/s43037-025-00478-7
  • 8. Federer, H.: Geometric measure theory. Springer, New York (1969)
  • 9. Feng, D., Huang, W.: Variational principles for topological entropies of subsets. J. Funct. Anal. 263, 2228–2254 (2012)
  • 10. Katok, A.: Lyapunov exponents, entropy and periodic orbits for diffeomorphisms. Inst. Hautes Études Sci. Publ. Math. 51, 137–173 (1980)
  • 11. Kawan, C.: Exponential state estimation, entropy and Lyapunov exponents. Systems Control Lett. 113, 78–85 (2018)
  • 12. Kifer, Y.: On the topological pressure for random bundle transformations. Amer. Math. Soc. Transl. 202, 197–214 (2001)
  • 13. Kolmogorov, A.: A new metric invariant of transient dynamical systems and automorphisms of Lebesgue spaces. Dokl. Akad. Sci. SSSR 119,...
  • 14. Liberzon, D., Mitra, S.: Entropy and minimal bit rates for state estimation and model detection. IEEE Trans. Automat. Control 63, 3330–3344...
  • 15. Mattila, P.: Geometry of sets and measures in Euclidean spaces. Cambridge University Press (1995)
  • 16. Pesin, Y.: Dimension theory in dynamical systems. Contemporary views and applications. University of Chicago Press, Chicago (1997)
  • 17. Pesin, Y., Pitskel, B.: Topological pressure and the variational principle for noncompact sets. Funct. Anal. Appl. 18, 307–318 (1984)
  • 18. Ruelle, D.: Statistical mechanics on a compact set with Zv action satisfying expansiveness and specification. Trans. Amer. Math. Soc....
  • 19. Ruelle, D.: Repellers for real analytic maps. Erg. Th. Dynam. Syst. 2, 99–107 (1982)
  • 20. Sinai, Y.: On the concept of entropy for a dynamical system. Dokl. Akad. Nauk SSSR 124, 768–771 (1959)
  • 21. Thieullen, P.: Généralisation du théorème de Pesin pour l’α-entropie, Lyapunov exponents (Oberwolfach,: Lecture Notes in Math., Vol. 1486....
  • 22. Tricot, C.: Two definitions of fractional dimension. Math. Proc. Cambridge Phil. Soc. 91, 57–74 (1982)
  • 23. Walters, P.: An introduction to ergodic theory. Springer, New York (1982)
  • 24. Wang, C., Chen, E.: Variational principles for BS dimension of subsets. Dynam. Syst. 27, 359–385 (2012)
  • 25. Wang, T.: Some notes on topological and measure-theoretic entropy. Qual. Theory Dyn. Syst. 20, 13 (2021)
  • 26. Xie, Y., Gao, F., Ye, M.: Variational principles for α-estimation topological pressure. Qual. Theory Dyn. Syst. 24, 174 (2025)
  • 27. Yang, R., Chen, E., Zhou, X.: Bowen’s equations for upper metric mean dimension with potential. Nonlinearity 35, 4905–4938 (2022)
  • 28. Yang, R., Chen, E., Zhou, X.: Variational principle for neutralized Bowen topological entropy. Qual. Theory Dyn. Syst. 23, 162 (2024)
  • 29. Zheng, D., Chen, E.: Bowen entropy for actions of amenable groups. Israel J. Math. 212, 895–911 (2016)
  • 30. Zhong, X., Chen, Z.: A variational principle for Bowen estimation entropy. Sci. Sin. Math. (in Chinese) 50, 1–12 (2020)
  • 31. Zhong, X., Chen, Z.: Variational principles for topological pressures on subsets. Nonlinearity 36, 1168–1191 (2023)