Spectral spread and non-autonomous Hamiltonian diffeomorphisms
arXiv:1805.01489 · doi:10.1007/s00229-018-1078-0
Abstract
For any symplectic manifold, Hamiltonian diffeomorphism group contains a subset which consists of times one flows of autonomous(time-independent) Hamiltonian vector fields. Polterovich and Shelukhin proved that the complement of autonomous Hamiltonian diffeomorphisms is dense in C^/infty-topology and Hofer's metric if the symplectic manifold is closed symplectically aspherical. In this paper, we generalize above theorem to general closed symplectic manifolds and general convex symplectic manifolds.