English

V-shaped action functional with delay

Symplectic Geometry 2023-04-26 v1

Abstract

In this note we introduce the V-shaped action function with delay in a symplectization which is an intermediate action functional between Rabinowitz action functional and the V-shaped action functional. It lives on the same space as the V-shaped action functional but its gradient flow equation is a delay equation as in the case of Rabinowitz action functional. We show that there is a smooth interpolation between the V-shaped action functional and the V-shaped action functional with delay during which the critical points and its actions are fixed. On the other hand there is a bijection between gradient flow lines of the V-shaped action functional with delay and the ones of Rabinowitz action functional.

Cite

@article{arxiv.2206.06735,
  title  = {V-shaped action functional with delay},
  author = {Urs Frauenfelder},
  journal= {arXiv preprint arXiv:2206.06735},
  year   = {2023}
}

Comments

14 pages

R2 v1 2026-06-24T11:50:32.710Z