V-Shaped Action Functional with Delay

IF 0.8 4区数学 Q3 MATHEMATICS, APPLIED

Regular and Chaotic Dynamics Pub Date : 2023-04-10 DOI:10.1134/S1560354723510020

Urs Frauenfelder

引用次数: 0

Abstract

In this note we introduce the V-shaped action functional with delay in a symplectization, which is an intermediate action functional between the 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 the 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. Moreover, we prove that there is a bijection between gradient flow lines of the V-shaped action functional with delay and the ones of the Rabinowitz action functional.

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具有延迟的V形作用函数

在这篇注释中，我们引入了在共选择中具有延迟的V形作用泛函，它是Rabinowitz作用泛函和V形作用函数之间的中间作用泛函。它与V形作用泛函生活在同一空间上，但它的梯度流方程是一个延迟方程，就像Rabinowitz作用泛函的情况一样。我们证明了在临界点及其作用是固定的情况下，V形作用泛函和带延迟的V形作用函数之间存在光滑的插值。此外，我们还证明了具有延迟的V形作用泛函的梯度流线与Rabinowitz作用泛函的斜率流线之间存在双射。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Regular and Chaotic Dynamics 物理-力学

CiteScore

2.50

自引率

7.10%

发文量

审稿时长

>12 weeks

期刊介绍： Regular and Chaotic Dynamics (RCD) is an international journal publishing original research papers in dynamical systems theory and its applications. Rooted in the Moscow school of mathematics and mechanics, the journal successfully combines classical problems, modern mathematical techniques and breakthroughs in the field. Regular and Chaotic Dynamics welcomes papers that establish original results, characterized by rigorous mathematical settings and proofs, and that also address practical problems. In addition to research papers, the journal publishes review articles, historical and polemical essays, and translations of works by influential scientists of past centuries, previously unavailable in English. Along with regular issues, RCD also publishes special issues devoted to particular topics and events in the world of dynamical systems.