On the family of trajectories of an analytic gradient flow converging to a critical point

TL;DR

This paper establishes sufficient conditions under which an analytic gradient flow has an infinite family of trajectories converging to a critical point, enhancing understanding of flow behavior near critical points.

Contribution

It introduces new criteria for the existence of infinite trajectory families in analytic gradient flows converging to critical points.

Findings

Identifies conditions ensuring infinite trajectories converge to critical points

Provides theoretical framework for analyzing gradient flow dynamics

Enhances understanding of flow behavior near critical points

Abstract

There are presented sufficient conditions for existence of an infinite family of trajectories of an analytic gradient flow which converge to a critical point.