A note on measure and expansiveness on uniform spaces

[摘要] We prove that the set of points doubly asymptotic to a point has measure zero with respect to any expansive outer regular measure for a bi-measurable map on a separable uniform space.  Consequently, we give a class of measures which cannot be expansive for Denjoy home-omorphisms on S 1 .  We then investigate the existence of expansive measures for maps with various dynamical notions. We further show that measure expansive (strong measure expansive) homeomorphisms with shadowing have periodic (strong periodic) shadowing. We relate local weak specification and periodic shadowing for strong measure expansive systems.

[学科分类] 几何与拓扑

[关键词] expansiveness;measure expansiveness;expansive measures;equicontinuity;shadowing;specification