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Finding normally hyperbolic invariant manifolds in two and three degrees of freedom with Hénon-Heiles-type potential

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Original languageEnglish
Article number022204
Number of pages15
JournalPhysical Review E
Volume100
DOIs
DateAccepted/In press - 22 Apr 2019
DatePublished (current) - 5 Aug 2019

Abstract

We present a method based on a Lagrangian descriptor for revealing the high-dimensional phase space structures that are of interest in nonlinear Hamiltonian systems with index-1 saddle. These phase space structures include a normally hyperbolic invariant manifold and its stable and unstable manifolds, which act as codimension-1 barriers to phase space transport. In this article, finding the invariant manifolds in high-dimensional phase space will constitute identifying coordinates on these invariant manifolds. The method of Lagrangian descriptor is demonstrated by applying to classical two and three degrees of freedom Hamiltonian systems which have implications for myriad applications in chemistry, engineering, and physics.

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    Rights statement: This is the final published version of the article (version of record). It first appeared online via American Physical Society at https://journals.aps.org/pre/abstract/10.1103/PhysRevE.100.022204 . Please refer to any applicable terms of use of the publisher.

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