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One of the fundamental results of ergodic optimization asserts that for any dynamical system on a compact metric space with the specification property and for a generic continuous function f every invariant probability measure that maximizes the space average of f must have zero entropy. We establish the analogical result in the context of constrained ergodic optimization, which is introduced by Garibaldi and Lopes, Functions for relative maximization, Dyn. Syst. 22(4) (2007), pp. 511-528.
Motonaga et al. (Thu,) studied this question.
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