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• W2166473876 abstract "Let ([sum ] A , T ) be a topologically mixing subshift of finite type on an alphabet consisting of m symbols and let Φ:[sum ] A → R d be a continuous function. Denote by σ Φ ( x ) the ergodic limit lim n →∞ n −1 [sum ] n −1 j =0 Φ( T j x ) when the limit exists. Possible ergodic limits are just mean values ∫ Φ d μ for all T -invariant measures. For any possible ergodic limit α, the following variational formula is proved: [formula here] where h μ denotes the entropy of μ and h top denotes topological entropy. It is also proved that unless all points have the same ergodic limit, then the set of points whose ergodic limit does not exist has the same topological entropy as the whole space [sum ] A" @default.
• W2166473876 created "2016-06-24" @default.
• W2166473876 creator A5047524815 @default.
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• W2166473876 date "2001-08-01" @default.
• W2166473876 modified "2023-10-09" @default.
• W2166473876 title "RECURRENCE, DIMENSION AND ENTROPY" @default.
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• W2166473876 doi "https://doi.org/10.1017/s0024610701002137" @default.
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