Billiards: A singular perturbation limit of smooth Hamiltonian flows

Vered Rom-Kedar; D. Turaev

doi:10.1063/1.4722010

Billiards: A singular perturbation limit of smooth Hamiltonian flows

Vered Rom-Kedar
, D. Turaev

Department of Computer Science and Applied Mathematics

Weizmann Institute of Science

Research output: Contribution to journal › Article › peer-review

Abstract

Nonlinear multi-dimensional Hamiltonian systems that are not near integrable typically have mixed phase space and a plethora of instabilities. Hence, it is difficult to analyze them, to visualize them, or even to interpret their numerical simulations. We survey an emerging methodology for analyzing a class of such systems: Hamiltonians with steep potentials that limit to billiards.

Original language	English
Article number	026102
Journal	Chaos
Volume	22
Issue number	2
DOIs	https://doi.org/10.1063/1.4722010
State	Published - 4 Apr 2012

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics
General Physics and Astronomy
Applied Mathematics

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10.1063/1.4722010

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title = "Billiards: A singular perturbation limit of smooth Hamiltonian flows",

abstract = "Nonlinear multi-dimensional Hamiltonian systems that are not near integrable typically have mixed phase space and a plethora of instabilities. Hence, it is difficult to analyze them, to visualize them, or even to interpret their numerical simulations. We survey an emerging methodology for analyzing a class of such systems: Hamiltonians with steep potentials that limit to billiards.",

author = "Vered Rom-Kedar and D. Turaev",

note = "Israel Science Foundation [273/07]; Minerva foundation; Leverhulme Trust [RPG-279]; LMS [41039]; ICL Math. Platform Grant (EPSRC)The authors thank the support of the Israel Science Foundation (Grant No. 273/07). V.R.K. acknowledges the support of the Minerva foundation, D.T. acknowledges the support of Leverhulme Trust Grant No. RPG-279, LMS Grant No. 41039, and the ICL Math. Platform Grant (EPSRC).",

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N1 - Israel Science Foundation [273/07]; Minerva foundation; Leverhulme Trust [RPG-279]; LMS [41039]; ICL Math. Platform Grant (EPSRC)The authors thank the support of the Israel Science Foundation (Grant No. 273/07). V.R.K. acknowledges the support of the Minerva foundation, D.T. acknowledges the support of Leverhulme Trust Grant No. RPG-279, LMS Grant No. 41039, and the ICL Math. Platform Grant (EPSRC).

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N2 - Nonlinear multi-dimensional Hamiltonian systems that are not near integrable typically have mixed phase space and a plethora of instabilities. Hence, it is difficult to analyze them, to visualize them, or even to interpret their numerical simulations. We survey an emerging methodology for analyzing a class of such systems: Hamiltonians with steep potentials that limit to billiards.

AB - Nonlinear multi-dimensional Hamiltonian systems that are not near integrable typically have mixed phase space and a plethora of instabilities. Hence, it is difficult to analyze them, to visualize them, or even to interpret their numerical simulations. We survey an emerging methodology for analyzing a class of such systems: Hamiltonians with steep potentials that limit to billiards.

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U2 - 10.1063/1.4722010

DO - 10.1063/1.4722010

M3 - مقالة

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VL - 22

JO - Chaos

JF - Chaos

IS - 2

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ER -

Billiards: A singular perturbation limit of smooth Hamiltonian flows

Abstract

ASJC Scopus subject areas

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