2016
DOI: 10.1088/0951-7715/30/1/13
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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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Cited by 14 publications
(55 citation statements)
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“…In [40] the statement appears in a slightly different form, but the version presented here follows directly from the theory developed in [40]. The following proof is a small variation of the proof of the main technical result (Proposition 5.1) in Entov-Polterovich's [22].…”
Section: 1mentioning
confidence: 94%
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“…In [40] the statement appears in a slightly different form, but the version presented here follows directly from the theory developed in [40]. The following proof is a small variation of the proof of the main technical result (Proposition 5.1) in Entov-Polterovich's [22].…”
Section: 1mentioning
confidence: 94%
“…The motivation for this function comes from Aubry-Mather theory where it was discovered by Contreras-Iturriaga-Paternain [19, Corollary 1] that the Mather -function, associated to a convex Hamiltonian on the cotangent bundle of a closed manifold, can be defined in a similar way. The proof of Theorem 27 relies heavily on beautiful ideas due to Buhovsky-Entov-Polterovich [15], Entov-Polterovich [22] and Polterovich [40]. Of course this result is only useful if we can find reasonable lower bounds for ∶ .…”
Section: S "M "mentioning
confidence: 99%
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