Ergodic Optimization of Super-continuous Functions in the Shift
Dynamical Systems
2015-03-17 v2
Abstract
Ergodic Optimization is the process of finding invariant probability measures that maximize the integral of a given function. It has been conjectured that "most" functions are optimized by measures supported on a periodic orbit, and it has been proved in several separable spaces that an open and dense subset of functions is optimized by measures supported on a periodic orbit. We add to these positive results by presenting a non-separable space, the class of super-continuous functions, where the set of functions optimized by periodic orbit measures contains an open subset dense in super-continuous functions.
Cite
@article{arxiv.1101.2706,
title = {Ergodic Optimization of Super-continuous Functions in the Shift},
author = {Anthony Quas and Jason Siefken},
journal= {arXiv preprint arXiv:1101.2706},
year = {2015}
}