Necessary and sufficient condition of C0 flows on closed surfaces with isolated singular points having the pseudoorbit tracing property

Abstract

IN this letter we discuss the necessary and sufficient condition of C 0 flows on closed surfaces with isolated singular points having the pseudo-orbit tracing property. According to ref. [1], on a closed surface, every minimal set of a C r ( r ≥2) flow is trivial, but it is possible for a C~0 flow to contain non-trivial minimal sets. Thus C 0 flows on closed surfaces are more complicated than C r ( r ≥2) flows....