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arXiv · 2206.06735

V-shaped action functional with delay

Urs Frauenfelder
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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.

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Urs Frauenfelder. 2022-06-14. V-shaped action functional with delay. https://doi.org/10.1134/s1560354723510020

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