2011/01/14 by Quas, Anthony, Siefken, Jason
#37A05 #37B10 #37D20 (Primary) #37D35 #37E10 (Secondary) #Dynamical Systems (math.DS) #FOS: Mathematics
paper · doi:10.48550/arxiv.1101.2706
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.