Expansive flows on uniform spaces

Se-Hyun Ku

doi:10.3934/dcds.2021165

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2022, Volume 42, Issue 3: 1585-1598. Doi: 10.3934/dcds.2021165

This issue Previous Article Quantitative destruction of invariant circles Next Article

Expansive flows on uniform spaces

Se-Hyun Ku^,

Department of Mathematics, Chungnam National University, Daejeon 34134, Republic of Korea

^* Corresponding author: Se-Hyun Ku
^* Corresponding author: Se-Hyun Ku

Received: March 2021

Revised: September 2021

Early access: November 2021

Published: March 2022

The author was supported by Basic Science Research Program through the National Research Foundation of Korea(NRF) funded by the Ministry of Education(NRF-2018R1D1A1B07051286) and by the National Research Foundation of Korea(NRF) grant funded by the Korea government (MSIT) (No. 2021R1C1C2011737).

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Abstract

In this paper we study several dynamical properties on uniform spaces. We define expansive flows on uniform spaces and provide some equivalent ways of defining expansivity. We also define the concept of expansive measures for flows on uniform spaces. We prove for flows on compact uniform spaces that every expansive measure vanishes along the orbits and has no singularities in the support. We also prove that every expansive measure for flows on uniform spaces is aperiodic and is expansive with respect to time-$ T $ map. Furthermore we show that every expansive measure for flows on compact uniform spaces maintains expansive under topological equivalence.

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Mathematics Subject Classification: Primary: 37B05; Secondary: 37C10, 54E15.

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