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 is an element of N\{0}, let L-n: X -> M(X) denote the n-th empirical measure, i.e.,
L(n)x = 1/n Sigma(n-1)(k=0)delta(Tkx).
A continuous affine deformation of L-n is a pair (Y, Xi) where Y is a vector space with linear compatible metric and Xi : M(X) -> Y is a continuous and affine map. This article is devoted to investigating the packing entropy of
{x is an element of X vertical bar A(Xi L(n)x) = C}
and
{x is an element of X vertical bar A(Xi L(n)x) subset of C},
in a dynamical system with the specification property and the positive expansive property, where C is a convex and closed subset of Xi (M( X, T)).
關聯:
DYNAMICAL SYSTEMS-AN INTERNATIONAL JOURNAL 卷: 27 期: 3 頁數: 387-402
