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arXiv · 2507.11048

Entropy Flexibility of Dynamical Systems

Alexander Arbieto·Piotr Oprocha·Elias Rego
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Abstract

Inspired by Katok's intermediate entropy property [Inst. Hautes \'Etudes Sci. Publ. Math. 51 (1980), 137-173], we introduce and study the notion of entropy flexibility for discrete-time and continuous-time dynamical systems. By using renewal systems techniques, we show that this property is present in several classes of systems where any intermediate value of entropy can be attained on a strictly ergodic sub-system. In addition, we prove an entropy flexibility analogue of Katok's conjecture: Entropy flexibility is a typical property for vector fields on 3-manifolds and surface diffeomorphisms.

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Alexander Arbieto, Piotr Oprocha, Elias Rego. 2025-07-15. Entropy Flexibility of Dynamical Systems. https://arxiv.org/abs/2507.11048

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