Lagrangian tetragons and instabilities in Hamiltonian dynamics

Michael Entov; Leonid Polterovich

doi:https://doi.org/10.1088/0951-7715/30/1/13

Lagrangian tetragons and instabilities in Hamiltonian dynamics

Michael Entov, Leonid Polterovich

Technion - Israel Institute of Technology, Tel Aviv University

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

Abstract

We present a new existence mechanism, based on symplectic topology, for orbits of Hamiltonian flows connecting a pair of disjoint subsets in the phase space. The method involves function theory on symplectic manifolds combined with rigidity of Lagrangian submanifolds. Applications include superconductivity channels in nearly integrable systems and dynamics near a perturbed unstable equilibrium.

Original language	English
Pages (from-to)	13-34
Number of pages	22
Journal	Nonlinearity
Volume	30
Issue number	1
DOIs	https://doi.org/10.1088/0951-7715/30/1/13
State	Published - Jan 2017

Keywords

Hamiltonian system
Lagrangian submanifold
Poisson bracket
connecting trajectory
symplectic manifold

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Mathematical Physics
Physics and Astronomy(all)
Applied Mathematics

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https://doi.org/10.1088/0951-7715/30/1/13

Cite this

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title = "Lagrangian tetragons and instabilities in Hamiltonian dynamics",

abstract = "We present a new existence mechanism, based on symplectic topology, for orbits of Hamiltonian flows connecting a pair of disjoint subsets in the phase space. The method involves function theory on symplectic manifolds combined with rigidity of Lagrangian submanifolds. Applications include superconductivity channels in nearly integrable systems and dynamics near a perturbed unstable equilibrium.",

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AU - Polterovich, Leonid

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AB - We present a new existence mechanism, based on symplectic topology, for orbits of Hamiltonian flows connecting a pair of disjoint subsets in the phase space. The method involves function theory on symplectic manifolds combined with rigidity of Lagrangian submanifolds. Applications include superconductivity channels in nearly integrable systems and dynamics near a perturbed unstable equilibrium.

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KW - Lagrangian submanifold

KW - Poisson bracket

KW - connecting trajectory

KW - symplectic manifold

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M3 - مقالة

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JO - Nonlinearity

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Lagrangian tetragons and instabilities in Hamiltonian dynamics

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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