Ergodic optimization for beta-transformations
Ergodic optimization for beta-transformations $T_β(x)= βx \pmod 1$ is developed. If $β>1$ is a beta-number, or such that the orbit-closure of $1$ is not minimal, we show that the Typically Periodic Optimization Conjecture holds, establishing that there exists an open dense set of Hölder continuous functions such that for each function in this set ...
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