A note on measure and expansiveness on uniform spaces

Authors

  • Pramod Das University of Delhi
  • Tarun Das University of Delhi

DOI:

https://doi.org/10.4995/agt.2019.8843

Keywords:

expansiveness, measure expansiveness, expansive measures, equicontinuity, shadowing, specification

Abstract

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.

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Author Biographies

Pramod Das, University of Delhi

Department of Mathematics, Faculty of Mathematical Sciences

Tarun Das, University of Delhi

Department of Mathematics, Faculty of Mathematical Sciences

References

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Published

2019-04-01

How to Cite

[1]
P. Das and T. Das, “A note on measure and expansiveness on uniform spaces”, Appl. Gen. Topol., vol. 20, no. 1, pp. 19–31, Apr. 2019.

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Articles