Dynamics of the Morse vector field
Differential Geometry
2026-02-24 v2
Abstract
The (negative) gradient vector fields of Morse functions on a compact manifold provide an important example in dynamical system. In this note we prove two important properties of this kind of vector field: Connectedness of critical points through orbits and exponential shrinkage of the flow on stable submanifolds. We also find applications in showing some vanishing results of maps or curvature operators.
Cite
@article{arxiv.2512.23268,
title = {Dynamics of the Morse vector field},
author = {Yijian Zhang},
journal= {arXiv preprint arXiv:2512.23268},
year = {2026}
}