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arXiv · 1704.05616

Ergodic Maximizing Measures of Non-Generic, Yet Dense Continuous Functions

Mao Shinoda
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Abstract

Ergodic optimization aims to single out dynamically invariant Borel probability measures which maximize the integral of a given "performance" function. For a continuous self-map of a compact metric space and a dense set of continuous performance functions, we show that the existence of uncountably many ergodic maximizing measures. We also show that, for a topologically mixing subshift of finite type and a dense set of continuous functions there exist uncountably many ergodic maximizing measures which are fully supported and have positive entropy.

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Mao Shinoda. 2017-04-19. Ergodic Maximizing Measures of Non-Generic, Yet Dense Continuous Functions. https://arxiv.org/abs/1704.05616

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