The entropy formula of shrinking target problem in nonautonomous dynamical systems

Abstract

This paper is devoted to studying the topological entropy of shrinking target problem in nonautonomous dynamical systems (NDSs). After providing the shrinking target problem of the topological version in NDSs, we obtain a general formula for computing the topological entropy of it. More precisely, we show that the entropy distribution principle still holds in NDSs and apply it to estimate the lower bound of the formula. In addition to the specification property, the concept of control non-decreasing property about the Bowen metric proposed by us is taken as a supplementary condition. Furthermore, we get the connection about the topological entropy between the shrinking target problem and the whole system. This extends the result of Ma et al. [Discrete Contin. Dyn. Syst. 39(5) (2019), pp. 2455–2471], corresponding to the case when the maps are the same as the more general case of different maps.

Keywords:

• Topological entropy
• nonautonomous dynamical systems
• shrinking target problem
• specification property

2020 Mathematics Subject Classifications:

• Primary: 37B55
• 37B40
• Secondary:37A44

Acknowledgments

The authors really appreciate the referees' valuable remarks and suggestions that helped a lot.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Correction Statement

This article has been corrected with minor changes. These changes do not impact the academic content of the article.