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- W2068620152 abstract "Let X be a compact metric space, f a continuous transformation on X, and Y a vector space with linear compatible metric. Denote by M(X) the collection of all the probability measures on X. For a positive integer n, define the nth empirical measure as[ L_{n}x=frac{1}{n}sum _{k=0}^{n-1}delta_{f^{k}x}, ]where is continuous and affine with respect to the weak topology on M(X). We think of the composite[ Xicirc L_{n}:X xrightarrow{L_n} M(X)xrightarrow{Xi} Y ]as a continuous and affine deformation of the empirical measure Ln. The set of divergence points of such a deformation is defined as[ D(f,Xi)={xin Xmid mbox{the limit of }Xi L_n x mbox{ does not exist}}. ]In this paper we show that for a continuous transformation satisfying the specification property, if is not a singleton, then the set of divergence points has full topological entropy, i.e.[ h_{rm top}(D(f,Xi))=h_{rm top}(f). ]" @default.
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- W2068620152 date "2005-05-19" @default.
- W2068620152 modified "2023-09-29" @default.
- W2068620152 title "Topological entropy for divergence points" @default.
- W2068620152 doi "https://doi.org/10.1017/s0143385704000872" @default.
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