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<p>Hofmann and Stojanov introduced the notion of receptive entropy invariants as an extension of the concept of topological entropy in 1995. The goal of this paper is to utilize this concept and generalize it to the case of two regular systems. Therefore, such an entropy-like quantity will exhibit as an invariant of topological conjugacy. Some basic dynamical propositions are also discussed. Finally, we provide examples to illustrate this receptive entropy value. For the doubling map and the tripling map on the unit circle, this paper demonstrates that the value is not equal to the topological entropy value of the product space.</p>

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Extended Receptive Entropy for Independent Actions

  • 期刊论文

  • 发表日期：

    2025年2月6日

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  • Wen-Chiao Cheng

摘要

Hofmann and Stojanov introduced the notion of receptive entropy invariants as an extension of the concept of topological entropy in 1995. The goal of this paper is to utilize this concept and generalize it to the case of two regular systems. Therefore, such an entropy-like quantity will exhibit as an invariant of topological conjugacy. Some basic dynamical propositions are also discussed. Finally, we provide examples to illustrate this receptive entropy value. For the doubling map and the tripling map on the unit circle, this paper demonstrates that the value is not equal to the topological entropy value of the product space.