Typical uniqueness in ergodic optimization
Abstract
Abstract For ergodic optimization on any topological dynamical system, with real-valued potential function f belonging to any separable Banach space V of continuous functions, we show that the f -maximizing measure is typically unique, in the strong sense that a countable collection of hypersurfaces contains the exceptional set of those f ∈ V with non-unique maximizing measure. This strengthens previous results asserting that the uniqueness set is both residual and prevalent. For various other topological vector spaces of continuous functions, we show that uniqueness of the maximizing measure is either generic, or prevalent, or corresponds to the complement of a sparse set.
Fields of Study & Subjects
Mathematical Dynamics and Fractals
Publication details
- Journal / source
- Nonlinearity
- Volume
- 39
- Issue
- 7
- Pages
- 075026–075026
- Publication date
- 28 July 2026
- Language
- EN