Ergodic measures of intermediate entropies for dynamical systems with the approximate product property

Abstract

For a dynamical system satisfying the approximate product property and asymptotically entropy expansiveness, we characterize a delicate structrue of the space of invariant measures: The ergodic measures of intermediate entropies and intermediate pressures are generic in certain subspaces. This proves a conjecture of Katok for a broad class of systems and extends a sequence of known results.

References in corpus (2)

• Topological and almost Borel Universality for systems with the weak specification property
• Unique ergodicity for zero-entropy dynamical systems with the approximate product property

Cited by in corpus (6)

• High pointwise emergence and Katok's conjecture for systems with non-uniform structure
• Unique ergodicity for zero-entropy dynamical systems with the approximate product property
• Zero-entropy dynamical systems with the gluing orbit property
• Equilibrium states of intermediate entropies
• Conditional intermediate entropy and Birkhoff average properties of hyperbolic flows
• Denseness of intermediate pressures for systems with the Climenhaga-Thompson structures