Ir al contenido

Documat


Remarks on Topological Entropy of Random Dynamical Systems

  • Li, Zhiming [1] ; Ding, Zhihui [1]
    1. [1] Northwest University

      Northwest University

      China

  • Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 17, Nº 3, 2018, págs. 609-616
  • Idioma: inglés
  • DOI: 10.1007/s12346-017-0258-8
  • Enlaces
  • Resumen
    • In this paper, we study several definitions of topological entropy (of noncompact or noninvariant bundles) for random transformations on a compact metric space. Furthermore their relationships are established.

  • Referencias bibliográficas
    • 1. Adler, R.L., Konheim, A.G., McAndrew, M.H.: Topological entropy. Trans. Am. Math. Soc. 114, 309–319 (1965)
    • 2. Arnold, L.: Random Dynamical Systems. Springer, Berlin (1998)
    • 3. Bogenschutz, T.: Entropy, pressure and a variational principle for random dynamical systems. Random Comput. Dyn. 1, 99–116 (1992)
    • 4. Bogenschutz, T.: Quilibrium States for Random Dynamical Systems, PhD. Thesis, Bremen University (1993)
    • 5. Bowen, R.: Entropy for group endomorphisms and homogeneous spaces. Trans. Am. Math. Soc. 153, 401–414 (1971)
    • 6. Bowen, R.: Periodic points and measures for axiom A diffeomorphims. Trans. Am. Math. Soc. 154, 377–397 (1971)
    • 7. Bowen, R.: Topological entropy for noncompact sets. Trans. Am. Math. Soc. 184, 125–136 (1973)
    • 8. Katok, A.: Fifty years of entropy in dynamics: 1958–2007. J. Mod. Dyn. 1(4), 545–596 (2007)
    • 9. Kawan, C.: Topological entropy—a survey. Institut fr Mathematik Universitat Augsburg 86, 1–35 (2011)
    • 10. Kifer, Y.: Ergodic Theory of Random Transformations. Birkhauser, Basel (1986)
    • 11. Kifer, Y.: On the topological pressure for random bundle transformations. Transl. Am. Math. Soc. Ser. 2(202), 197–214 (2001)
    • 12. Kifer, Y., Liu, P.-D.: Random dynamical systems. Handb. Dyn. Syst. 1B, 379–499 (2006)
    • 13. Li, Z.-M.: Remarks on topological entropy of nonautonomous dynamical systems. Int. J. Bifurc. Chaos 25(12), 1550158 (2015)
    • 14. Liu, P.-D., Qian, M.: Smooth Ergodic Theory of Random Dynamical Systems, Lecture Notes in Mathematics, 1606. Springer, Berlin (1995)
    • 15. Pesin, Y., Pitskel, B.S.: Topological pressure and the variational principle for noncompact sets. Funct. Anal. Its Appl. 18, 307–318 (1984)
    • 16. Pesin, Y.: Dimension Theory in Dynamical Systems: Contemporary Views and Applications. University of Chicago Press, Chicago (2008)
    • 17. Walters, P.: An Introduction to Ergodic Theory, Graduate Texts in Mathematics, vol. 79. Springer, New York (1982)
    • 18. Zhu, Y.-J.: Two notes on measure-theoretic entropy of random dynamical systems. Acta Math. Sin. 25, 961–970 (2009)

Fundación Dialnet

Mi Documat

Opciones de artículo

Opciones de compartir

Opciones de entorno