Packing entropy and divergence points

摘要

Let (X, d, T) be a dynamical system, where (X, d) is a compact metric space and T: X→X is a continuous map. For n ∈ N{0}, let L_n,: X→ M(X) denote the n-th empirical measure, i.e.,rnL_nx=1Σ_(k=0)~(n-1)δT~kxrnA continuous affine deformation of L_n, is a pair (Y, Ξ) where Y is a vector space with linear compatible metric and Ξ: M(X)→ Y is a continuous and affine map. This article is devoted to investigating the packing entropy ofrn{x ∈ XA(ΞL_nx) = C}rnandrn{x ∈ XA(ΞL_nx) c C},rnin a dynamical system with the specification property and the positive expansive property, where C is a convex and closed subset of Ξ(M(X, T)).