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Expansive flows on uniform spaces

  • * Corresponding author: Se-Hyun Ku

    * Corresponding author: Se-Hyun Ku

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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  • 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.

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


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