Remarks on Metric Entropy of Random Z 2 Actions on a Non-compact Space

• Li, Zhiming ^[1] ; Tang, Dingxuan ^[1]
  1. [1] Northwest University

     Northwest University

     China

     
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 18, Nº 2, 2019, págs. 405-412
• Idioma: inglés
• DOI: 10.1007/s12346-018-0292-1
• Enlaces
  • Texto completo
• Resumen

  • In this paper, we establish Brin–Katok local entropy and Katok δ entropy formula of random Z2 transformations on a non-compact space.

• Referencias bibliográficas
  • 1. Arnold, L.: Random Dynamical Systems. Springer, Berlin (1998)
  • 2. Bogenschutz, T.: Entropy, pressure and a variational principle for random dynamical systems. Random Comput. Dyn. 1, 99–116 (1992)
  • 3. Bogenschutz, T.: Equilibrium states for random dynamical system, PhD. Thesis, Bremen University (1993)
  • 4. Brin, M., Katok, A.: On Local Entropy. Lecture Notes in Mathematics, vol. 1007, pp. 30–38. Springer, Berlin (1983)
  • 5. Crauel, H.: Random probability measures on polish spaces, Habilitationsschrift. Universitat, Bremen (1995)
  • 6. Dooley, A.H., Zhang, G.: Local Entropy Theory of a Random Dynamical System, vol. 233, p. 1099. Memoirs of the American Mathematical Society,...
  • 7. Katok, A.: Fifty years of entropy in dynamics: 1958–2007. J. Mod. Dyn. 1, 545–596 (2007)
  • 8. Katok, A.: Lyapunov exponents, entroy and periodic orbits for diffeomorphisms. Inst. Hautes Etudes Sci. Publ. Math. 51, 137–173 (1980)
  • 9. Kifer, Y.: Ergodic Theory of Random Transformations. Birkhauser, Basel (1986)
  • 10. Kifer, Y.: Multidimensional random subshifts of finite type and their large deviations. Probab. Theory Relat. Fields 103, 223–248 (1995)
  • 11. Kifer, Y., Liu, P.-D.: Random dynamical systems. In: Hasselblatt, B., Katok, A. (eds.) Handbook of Dynamical Systems, pp. 379–499. Elsevier,...
  • 12. Li, Z., Shu, L.: The metric entropy of random dynamical Systems in a Banach space: Ruelle inequality. Ergod. Theory Dyn. Syst. 34(02),...
  • 13. Li, Z., Ding, Z.: Remarks on topological entropy of random dynamical systems. Qual. Theory Dyn. Syst. 17(03), 609–616 (2018)
  • 14. Liu, P.-D., Qian, M.: Smooth Ergodic Theory of Random Dynamical Systems. Lecture Notes in Mathematics, vol. 1606. Springer, Berlin (1995)
  • 15. Walters, P.: An Introduction to Ergodic Theory. Springer, Berlin (1982)
  • 16. Yujun, Z.: Two notes on measure-theoretic entropy of random dynamical systems. Acta Math. Sinica Engl. Ser. 25(6), 961–970 (2009)
  • 17. Zhu, Y.: Entropy formula for random Zk -actions. Trans. Am. Math. Soc. 369, 4517–4544 (2017)
  • 18. Zhu, Y.: A note on two types of Lyapunov exponents and entropies for Zk -actions. J. Math. Anal. Appl. 461, 38–50 (2018)