English

Prevalent uniqueness in ergodic optimisation

Dynamical Systems 2020-03-20 v1

Abstract

One of the fundamental results of ergodic optimisation asserts that for any dynamical system on a compact metric space XX and for any Banach space of continuous real-valued functions on XX which embeds densely in C(X)C(X) there exists a residual set of functions in that Banach space for which the maximising measure is unique. We extend this result by showing that this residual set is additionally prevalent, answering a question of J. Bochi and Y. Zhang.

Keywords

Cite

@article{arxiv.2003.08762,
  title  = {Prevalent uniqueness in ergodic optimisation},
  author = {Ian D. Morris},
  journal= {arXiv preprint arXiv:2003.08762},
  year   = {2020}
}