On the finiteness of uniform sinks

Abstract

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