Expansive flows on uniform spaces

Abstract

<p style='text-indent:20px;'>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-<inline-formula><tex-math id="M1">\begin{document}$ T $\end{document}</tex-math></inline-formula> map. Furthermore we show that every expansive measure for flows on compact uniform spaces maintains expansive under topological equivalence.</p>