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Abstract
In this paper we introduce the topological entropy and the capacity topological entropies of non-autonomous iterated function systems, which extends the notion of the topological entropy of non-autonomous iterated function systems (or NAIFSs for short) on countably infinite alphabets, by using the Carathéodory–Pesin structure (C-P structure). We provide some properties of these notions and give the main results. In fact we give lower and upper estimations of the topological entropy of non-autonomous iterated function systems action by local entropies.
Acknowledgments
The authors thank the referees for their valuable suggestions and comments.
Disclosure statement
No potential conflict of interest was reported by the author(s).
Additional information
Funding
The work was supported by the Foundation in Higher Education Institutions of Henan Province, PR China (grant number 23A110020). The second author was sponsored by ‘Chenguang Program’ (20CGB09) supported by Shanghai Education Development Foundation and Shanghai Municipal Education Commission; The work was supported by the Jiangsu Province Postgraduate Research and Innovation Program (KYCX23_3300).