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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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Finding normally hyperbolic invariant manifolds in two and three degrees of freedom with Hénon-Heiles-type potential. / Naik, Shibabrat; Wiggins, Stephen.

In: Physical Review E, Vol. 100, 022204, 05.08.2019.

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@article{e086aef3165b49e7ad8fcd3572f37dd3,
title = "Finding normally hyperbolic invariant manifolds in two and three degrees of freedom with H{\'e}non-Heiles-type potential",
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.",
author = "Shibabrat Naik and Stephen Wiggins",
year = "2019",
month = "8",
day = "5",
doi = "10.1103/PhysRevE.100.022204",
language = "English",
volume = "100",
journal = "Physical Review E",
issn = "2470-0045",
publisher = "American Physical Society (APS)",

}

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TY - JOUR

T1 - Finding normally hyperbolic invariant manifolds in two and three degrees of freedom with Hénon-Heiles-type potential

AU - Naik, Shibabrat

AU - Wiggins, Stephen

PY - 2019/8/5

Y1 - 2019/8/5

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85070553706&partnerID=8YFLogxK

U2 - 10.1103/PhysRevE.100.022204

DO - 10.1103/PhysRevE.100.022204

M3 - Article

VL - 100

JO - Physical Review E

JF - Physical Review E

SN - 2470-0045

M1 - 022204

ER -