- Journal Article
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. © 2020 World Scientific Publishing Company. Show more
Journal / seriesJournal of Topology and Analysis
Pages / Article No.
PublisherWorld Scientific Publishing
SubjectGradient trajectory; Birth-death singularity; Existence and uniqueness
156000 - Lagrangian Cobordism, Symplectic Dynamics and Infinite Dimensional Group Actions (SNF)
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