A Note on Specification Property of Dynamical Systems
Volume 4, Issue 2, June 2018, Pages: 34-38
Received: Apr. 20, 2018;
Accepted: May 22, 2018;
Published: Jun. 28, 2018
Views 793 Downloads 99
Nan Li, School of Mathematical Science, Dalian University of Technology, Dalian, China
Lidong Wang, School of Mathematical Science, Dalian University of Technology, Dalian, China; School of Science, Dalian Nationalities University, Dalian, China; The College of Public Foundation and Innovation and Entrepreneurship, Zhuhai College of Jilin University, Zhuhai, China
Fengchun Lei, School of Mathematical Science, Dalian University of Technology, Dalian, China
Follow on us
The paper is discussed the sensitive and transitive property of a dynamical system with strong specification property. It is proved that if a dynamical system is sensitive, then it is syndetically sensitive with the same constant of sensitivity. Further, it is given another condition such that if a dynamical system is sensitive, then it is syndetically sensitive with the same constant of sensitivity. Meanwhile, it is stated that if a dynamical system has shadowing property, then it is totally syndetically transitive.
Sensitive, Specification Property, Syndetically Transitive
To cite this article
A Note on Specification Property of Dynamical Systems, Mathematics Letters.
Vol. 4, No. 2,
2018, pp. 34-38.
Copyright © 2018 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/
) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Bowen R. (1971). Periodic points and measures for axiom a diffeomorphisms, trans, Trans. Amer. Math. Soc. 154, 377–397.
Lampart M., Oprocha P. (2009). Shift spaces, ω-chaos and specification property, Topology & Its Applications 156 (18), 2979–2985.
Kulczycki M., Kwietniak D., Oprocha P. (2013). On almost specification and average shadowing properties, Fundamenta Mathematicae 224 (3), 241–278.
Lidong. W., Hui. W., Guifeng. H. (2014). Minimal sets and ω-chaos in expansive systems with weak specification property, Discrete & Continuous Dynamical Systems 35 (3), 1231–1238.
Dong Y. (2015). Systems with almost specification property may have zero entropy, Fuzzy Sets & Systems 364 (10), 5395–5414.
Kwietniak D., Lacka M., Oprocha P. (2015). A panorama of specification-like properties and their consequences, Contemporary Mathematics arXiv: 1503.07355v2 [math. DS] 26 May. doi:10.1016/S0031-8. 914 (53) 80099-6.
Kwietniak D., Oprocha P., Rams M. (2016). On entropy of dynamical systems with almost specification, Israel Journal of Mathematics 213 (1), 475–503.
Shah S., Das R., Das T. (2016). Specification property for topological spaces, Journal of Dynamical & Control Systems 29 (7), 1–8.
Pfister C., Sullivan W. (2007). On the topological entropy of saturated sets, Ergodic Theory and Dynamical Systems 27 (3), 919–956.
Akin E., Glasner E. (2001). Residual properties and almost equicontinuity, Journald’ Analyse Mathmatique 84 (1), 243–286.
Wen. H., H. Li, Xiangdong. Y. (2012). Family independence for topological and measurable dynamics, Transactions of the American Mathematical Society 364 (10), 5209–5242.
Furstenberg H. (1981). Recurrence in ergodic theory and combinatorial number theory, Princeton University Press.
Xinxing W., Oprocha P., Guanrong C. (2016). On various definitions of shadowing with average error in tracin, Eprint Arxiv 29 (7), 942–1972.