On the stable set of an analytic gradient flow

[摘要] Let f : R-n -> R, n >= 2, be a real analytic function. In this paper we study the stable set of the gradient flow (x)over dot = del f(x) at a critical point of f. In particular we present simple topological conditions which imply that this set contains an infinite family of trajectories, or has a non-empty interior. (C) 2021 Elsevier Inc. All rights reserved.

[发布日期] 2021-11-15

[关键词] Trajectories of gradient flows;Critical points;Stable set