Global Hamiltonian dynamics on singular symplectic manifolds
Cédric Oms
Abstract:In this thesis, we study the Reeb and Hamiltonian dynamics on singular symplectic and contact manifolds. Those structures are motivated by singularities coming from classical mechanics and fluid dynamics.
We start by studying generalized contact structures where the non-integrability condition fails on a hypersurface, the critical hypersurface. Those structures, called $b$-contact structures, arise from hypersurfaces in $b$-symplectic manifolds that have been previously studied extensively in th… Show more
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