On the finiteness of uniform sinks

Abstract

We study the finiteness of uniform sinks for flow. Precisely, we prove that, for $α>0$ $T>0$, if a vector field $X$ has only hyperbolic singularities or sectionally dissipative singularities, then $X$ can have only finitely many $(α,T)$-uniform sinks. This is a generalized version of a theorem of Liao