On the generic behavior of the spectral norm

TL;DR

This paper proves that for most Hamiltonian diffeomorphisms on any closed symplectic manifold, the spectral norm of their iterates remains uniformly bounded away from zero, highlighting a generic stability property.

Contribution

It establishes a generic lower bound for the spectral norm of iterates of Hamiltonian diffeomorphisms on closed symplectic manifolds.

Findings

Spectral norm of iterates is generically bounded away from zero

Results hold for all closed symplectic manifolds

Highlights stability of Hamiltonian dynamics

Abstract

The main result of the paper is that for any closed symplectic manifold the spectral norm of the iterates of a Hamiltonian diffeomorphism is locally uniformly bounded away from zero $C^\infty$-generically.