Lagrangian tetragons and instabilities in Hamiltonian dynamics

TL;DR

This paper introduces a symplectic topology-based method to prove the existence of Hamiltonian orbits connecting disjoint phase space regions, with applications to superconductivity and unstable equilibria.

Contribution

It develops a novel existence mechanism using Lagrangian tetragons and symplectic topology, advancing understanding of Hamiltonian dynamics and instabilities.

Findings

Established new existence results for connecting orbits

Applied method to nearly integrable systems and unstable equilibria

Demonstrated relevance to superconductivity channels

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.