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