Spectral spread and non-autonomous Hamiltonian diffeomorphisms

TL;DR

This paper extends the understanding of Hamiltonian diffeomorphisms by demonstrating that non-autonomous Hamiltonian diffeomorphisms are dense in various classes of closed symplectic manifolds, broadening prior results.

Contribution

The authors generalize previous density results of non-autonomous Hamiltonian diffeomorphisms to all closed and convex symplectic manifolds.

Findings

Non-autonomous Hamiltonian diffeomorphisms are dense in the C^infty-topology.

Non-autonomous Hamiltonian diffeomorphisms are dense in Hofer's metric.

The results apply to a broader class of symplectic manifolds than previously known.

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.