Abstract
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.
Similar content being viewed by others
Change history
21 November 2017
In the original publication of the article, the last name of the second author was incorrect. The correct name of the author should read as “Zhihui Ding”.
References
Adler, R.L., Konheim, A.G., McAndrew, M.H.: Topological entropy. Trans. Am. Math. Soc. 114, 309–319 (1965)
Arnold, L.: Random Dynamical Systems. Springer, Berlin (1998)
Bogenschutz, T.: Entropy, pressure and a variational principle for random dynamical systems. Random Comput. Dyn. 1, 99–116 (1992)
Bogenschutz, T.: Quilibrium States for Random Dynamical Systems, PhD. Thesis, Bremen University (1993)
Bowen, R.: Entropy for group endomorphisms and homogeneous spaces. Trans. Am. Math. Soc. 153, 401–414 (1971)
Bowen, R.: Periodic points and measures for axiom A diffeomorphims. Trans. Am. Math. Soc. 154, 377–397 (1971)
Bowen, R.: Topological entropy for noncompact sets. Trans. Am. Math. Soc. 184, 125–136 (1973)
Katok, A.: Fifty years of entropy in dynamics: 1958–2007. J. Mod. Dyn. 1(4), 545–596 (2007)
Kawan, C.: Topological entropy—a survey. Institut fr Mathematik Universitat Augsburg 86, 1–35 (2011)
Kifer, Y.: Ergodic Theory of Random Transformations. Birkhauser, Basel (1986)
Kifer, Y.: On the topological pressure for random bundle transformations. Transl. Am. Math. Soc. Ser. 2(202), 197–214 (2001)
Kifer, Y., Liu, P.-D.: Random dynamical systems. Handb. Dyn. Syst. 1B, 379–499 (2006)
Li, Z.-M.: Remarks on topological entropy of nonautonomous dynamical systems. Int. J. Bifurc. Chaos 25(12), 1550158 (2015)
Liu, P.-D., Qian, M.: Smooth Ergodic Theory of Random Dynamical Systems, Lecture Notes in Mathematics, 1606. Springer, Berlin (1995)
Pesin, Y., Pitskel, B.S.: Topological pressure and the variational principle for noncompact sets. Funct. Anal. Its Appl. 18, 307–318 (1984)
Pesin, Y.: Dimension Theory in Dynamical Systems: Contemporary Views and Applications. University of Chicago Press, Chicago (2008)
Walters, P.: An Introduction to Ergodic Theory, Graduate Texts in Mathematics, vol. 79. Springer, New York (1982)
Zhu, Y.-J.: Two notes on measure-theoretic entropy of random dynamical systems. Acta Math. Sin. 25, 961–970 (2009)
Author information
Authors and Affiliations
Corresponding author
Additional information
The original version of this article has been revised. The last name of the second author was incorrect. Now, it has been corrected.
This research is supported by the National Natural Science Foundation of China under Grant No. 11301417 and Natural Science Foundation of Shaanxi Provincial Department of Education No. 17JK0755.
Rights and permissions
About this article
Cite this article
Li, Z., Ding, Z. Remarks on Topological Entropy of Random Dynamical Systems. Qual. Theory Dyn. Syst. 17, 609–616 (2018). https://doi.org/10.1007/s12346-017-0258-8
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12346-017-0258-8