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arXiv · 2603.29720

Entropy structures with continuous partitions of unity

Jérôme Carrand
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Abstract

Using only continuous partitions of unity, we provide equivalent definitions for the metric, topological and topological tail entropies and pressures of a continuous self-map of a compact set, as well as their conditional versions. A tail variational principle for these new definitions is proved. We extend Downarowicz's notions of candidates and entropy structures to account for almost-increasing sequences of functions arising from the new definitions. Finally, we deduce a partial answer to a question raised by Newhouse.

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Jérôme Carrand. 2026-03-31. Entropy structures with continuous partitions of unity. https://arxiv.org/abs/2603.29720

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