Gradient Flow Line Near Birth-Death Critical Points
Differential Geometry
2018-05-04 v3 Dynamical Systems
Symplectic Geometry
Abstract
Near a birth-death critical point in a one-parameter family of gradient flows, there are precisely two Morse critical points of index difference one on the birth side. This paper gives a self-contained proof of the folklore theorem that these two critical points are joined by a unique gradient trajectory up to time-shift. The proof is based on the Whitney normal form, a Conley index construction, and an adiabatic limit analysis for an associated fast-slow differential equation.
Cite
@article{arxiv.1706.07746,
title = {Gradient Flow Line Near Birth-Death Critical Points},
author = {Charel Antony},
journal= {arXiv preprint arXiv:1706.07746},
year = {2018}
}
Comments
39 pages, 4 figures