Recurrence, Dimension and Entropy

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On Khintchine exponents and Lyapunov exponents of continued fractions (2008, methodology): “ α} for a given α∈ R. The function f(α) := dim {x∈ X: φ(x) = α} is called the Birkhoﬀ spectrum for the function φ. When X is compact, T and φare continuous, the Birkhoﬀ spectrum are well studied (see [1, 14, 15] and the references therein. See also the book of Y. B. Pesin [35]). The main tool of our”
Higher-dimensional multifractal analysis (2002, background): “, 1) and f is a topologically mixing subshift of finite type, Fan, Feng and Wu [6] showed that (29) holds for an arbitrary continuous function Φ.”
Ergodic Limits on the Conformal Repellers (2002, background): “[14] had considered the setting on ðSA;sÞ; a subshift space of finite type.”
Lyapunov exponents for products of matrices and multifractal analysis. Part II: General matrices (2003, background): “Theorem A extends the corresponding results for the Birkho averages of scalar functions, for which one is referred to, e.g., [1, 2, 3, 9, 10 , 16, 35, 38, 40, 41, 47].”
Distribution of frequencies of digits via multifractal analysis (2002, methodology): “This first formula was obtained independently by Fan, Feng and Wu [9].”