On the stable set of an analytic gradient flow

2020/01/20 by Szafraniec, Zbigniew · 1 citation
#Algebraic Geometry (math.AG) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.2001.07192

Abstract

In this paper we study the stable set of the gradient flow associated with a critical point of an analytic function. In particular we present simple topological conditions which imply that this set contains an infinite family of trajectories, or has a non-empty interior.

Cited by

• Reachability of gradient dynamics

Related

• On the family of trajectories of an analytic gradient flow converging to a critical point
• Local behaviour of the gradient flow of an analytic function near the unstable set of a critical point
• Non-sufficiency of smoothness in the gradient conjecture
• A remark on fixed point sets of gradient-like flows
• On the Space of Trajectories of a Generic Vector Field