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math.DS2026
Typicality of periodic optimization over an expanding circle map
Rui Gao, Weixiao Shen, Ruiqin Zhang
We study the ergodic optimization problem over a real analytic expanding circle map. We show that in both the topological and the measure-theoretical senses, a typical perfor…
math.DS2025
Lyapunov maximizing measures for balanced pairs of matrices
Rui Gao
We show that every balanced pair (see Definition 1.1) of real matrices admits a unique Lyapunov maximizing measure, and the measure is always Sturmian.