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Topological Entropy, Topological Pressure and Topological Pseudo Entropy of Iterated Function Systems on Uniform Spaces

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Abstract

In this paper, we introduce the notions of topological entropy, topological pressure and topological pseudo-entropy of iterated function systems(IFS) on uniform spaces. We discuss these notions in three different ways using the idea of separated sets, spanning sets and open covers. We prove that the topological entropy given by the idea of separated sets is same as the topological entropy calculated using spanning sets and that of open covers. We also find that topological entropy is same as topological pseudo-entropy of iterated function systems in compact uniform spaces.

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Correspondence to Khundrakpam Binod Mangang.

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Singh, M.B., Devi, T.T., Mangang, K.B. et al. Topological Entropy, Topological Pressure and Topological Pseudo Entropy of Iterated Function Systems on Uniform Spaces. Qual. Theory Dyn. Syst. 23, 214 (2024). https://doi.org/10.1007/s12346-024-01074-0

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