Applications of Hofer's geometry to Hamiltonian dynamics

Details Applications of Hofer's geometry to Hamiltonian dynamics Applications of Hofer's geometry to Hamiltonian dynamics

2003-05-09

arxiv.org/abs/math/0305146v1

Mathematics

Symplectic Geometry

9 pages, 1 figure

Scientific paper

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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