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Applications of Hofer's geometry to Hamiltonian dynamics

Urs Frauenfelder·Felix Schlenk
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Abstract

We prove the following three results in Hamiltonian dynamics. 1. The Weinstein conjecture holds true for every displaceable hypersurface of contact type. 2. Every magnetic flow on a closed Riemannian manifold has contractible closed orbits for a dense set of small energies. 3. Every closed Lagrangian submanifold of an arbitrary symplectic manifold whose fundamental group injects and which admits a Riemannian metric without closed geodesics has the intersection property.

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Urs Frauenfelder, Felix Schlenk. 2003-05-09. Applications of Hofer's geometry to Hamiltonian dynamics. https://arxiv.org/abs/math/0305146

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