Ergodic maximization problem for expanding maps with differentiable observables
Dynamical Systems
2021-03-23 v2
Abstract
We show that for an expanding map, the maximizing measures of a generic (open and dense) () differentiable functions are supported on a single periodic orbit. [There is a gap in the discussions. For the approximation of the Lipschitz functions, we can only control the derivative, but we can not control the derivatives for . Elegant approximation methods might be needed to solve this problem.]
Keywords
Cite
@article{arxiv.2005.09164,
title = {Ergodic maximization problem for expanding maps with differentiable observables},
author = {X. Zhang},
journal= {arXiv preprint arXiv:2005.09164},
year = {2021}
}