Symplectic homology and periodic orbits near symplectic submanifolds (Q1884763)

It is shown that for a sufficiently small neighborhood of a compact symplectic submanifold in a geometrically bounded aspherical symplectic manifold \(W\) the symplectic homology does not vanish. This implies the following result along the lines of the theorem of Weinstein-Moser: if \(H:W\rightarrow \mathbb R\) is a smooth function which attains an isolated minimum on a compact symplectic submanifold \(M\), say \(H| _{M}=0\), then the levels \(\{H=\varepsilon\}\) carry contractible periodic orbits for a dense set of small values \(\varepsilon >0\). This theorem strengthens and complements some recent results. Also, as an application, a new existence theorem for twisted geodesic flows is obtained. This theorem implies the existence of contractible periodic orbits for a dense set of low energy values.