Ergodic Optimization of Super-continuous Functions in the Shift
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چکیده
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. All known positive results have been for separable spaces. We give in this paper the first positive result for a non-separable space, the space of supercontinuous functions on the full shift, where the set of functions optimized by periodic orbit measures contains an open dense subset.
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تاریخ انتشار 2011