A sufficient condition for the existence of Hamiltonian bifurcations with continuous isotropy

James Montaldi; Miguel Rodríguez-Olmos

doi:10.1007/s40306-012-0006-8

A sufficient condition for the existence of Hamiltonian bifurcations with continuous isotropy

James Montaldi, Miguel Rodríguez-Olmos

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Abstract

We present a framework for the study of the local qualitative dynamics of equivariant Hamiltonian flows specially designed for points in phase space with non-trivial isotropy. This is based on the classical construction of structure-preserving tubular neighborhoods for Hamiltonian Lie group actions on symplectic manifolds. This framework is applied to obtaining concrete and testable conditions guaranteeing the existence of bifurcations from symmetric branches of Hamiltonian relative equilibria. © 2013 Institute of Mathematics, Vietnam Academy of Science and Technology (VAST) and Springer Science+Business Media Singapore.

Original language	English
Pages (from-to)	11-19
Number of pages	8
Journal	Acta Mathematica Vietnamica
Volume	38
Issue number	1
DOIs	https://doi.org/10.1007/s40306-012-0006-8
Publication status	Published - Mar 2013

Keywords

Hamiltonian bifurcations
Momentum maps
Relative equilibria
Symmetry breaking

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abstract = "We present a framework for the study of the local qualitative dynamics of equivariant Hamiltonian flows specially designed for points in phase space with non-trivial isotropy. This is based on the classical construction of structure-preserving tubular neighborhoods for Hamiltonian Lie group actions on symplectic manifolds. This framework is applied to obtaining concrete and testable conditions guaranteeing the existence of bifurcations from symmetric branches of Hamiltonian relative equilibria. {\textcopyright} 2013 Institute of Mathematics, Vietnam Academy of Science and Technology (VAST) and Springer Science+Business Media Singapore.",

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AB - We present a framework for the study of the local qualitative dynamics of equivariant Hamiltonian flows specially designed for points in phase space with non-trivial isotropy. This is based on the classical construction of structure-preserving tubular neighborhoods for Hamiltonian Lie group actions on symplectic manifolds. This framework is applied to obtaining concrete and testable conditions guaranteeing the existence of bifurcations from symmetric branches of Hamiltonian relative equilibria. © 2013 Institute of Mathematics, Vietnam Academy of Science and Technology (VAST) and Springer Science+Business Media Singapore.

KW - Hamiltonian bifurcations

KW - Momentum maps

KW - Relative equilibria

KW - Symmetry breaking

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JO - Acta Mathematica Vietnamica

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A sufficient condition for the existence of Hamiltonian bifurcations with continuous isotropy

Abstract

Keywords

UN SDGs

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