Symplectic homology and periodic orbits near symplectic submanifolds

Symplectic Homology and Periodic Orbits near Symplectic Submanifolds

We show that a small neighborhood of a closed symplectic submanifold in a geometrically bounded aspherical symplectic manifold has nonvanishing symplectic homology. As a consequence, we establish the existence of contractible closed characteristics on any thickening of the boundary of the neighborhood. When applied to twisted geodesic flows on compact symplectically aspherical manifolds, this i...

Periodic Orbits near Symplectic Submanifolds

We show that a small neighborhood of a closed symplectic submanifold in a geometrically bounded aspherical symplectic manifold has nonvanishing symplectic homology. As a consequence, we establish the existence of contractible closed characteristics on any thickening of the boundary of the neighborhood. When applied to twisted geodesic flows on compact symplectically aspherical manifolds, this i...

Periodic Orbits of Hamiltonian Flows near Symplectic Critical Submanifolds

In this paper we produce a lower bound for the number of periodic orbits of certain Hamiltonian vector fields near Bott-nondegenerate symplectic critical submanifolds. This result is then related to the problem of finding closed orbits of the motion of a charged low energy particle on a Riemannian manifold under the influence of a magnetic field.

Symplectic Homology and Periodic Orbits Nearsymplectic Submanifoldskai

Realizing homology classes by symplectic submanifolds

In this note we prove that a positive multiple of each even-dimensional integral homology class of a compact symplectic manifold (M2n, ω) can be represented as the difference of the fundamental classes of two symplectic submanifolds in (M2n, ω). We also prove the realizability of some integral homology classes by symplectic submanifolds in (M2n, ω).