A note on measure and expansiveness on uniform spaces

Autor:	Pramod Das, Tarun Das
Jazyk:	angličtina
Rok vydání:	2019
Předmět:	expansiveness measure expansiveness expansive measures equicontinuity shadowing specification Mathematics QA1-939 Analysis QA299.6-433
Zdroj:	Applied General Topology, Vol 20, Iss 1, Pp 19-31 (2019)
Druh dokumentu:	article
ISSN:	1576-9402 1989-4147
DOI:	10.4995/agt.2019.8843
Popis:	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 S1. 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.
Databáze:	Directory of Open Access Journals
Externí odkaz:	https://doaj.org/article/2f435b59b96b41caa7904b5e79949501 Zobrazit plný text záznamu View record in DOAJ Plný text ve formátu PDF