This study demonstrates entropy flexibility in dynamical systems, highlighting its presence in ergodic sub-systems and 3-manifolds.
Inspired by Katok's intermediate entropy property [Inst. Hautes Études 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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Arbieto et al. (2025) studied this question.
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