Stably weakly shadowing symplectomorphisms are partially hyperbolic

Abstract

Let M be a closed, symplectic connected Riemannian manifold, f a symplectomorphism on M. We prove that if f is C1-stably weakly shadowing on M, then the whole manifold M admits a partially hyperbolic splitting.

9 pages

References in corpus (1)

• Volume Preserving Diffeomorphisms with Weak and Limit Weak Shadowing

Cited by in corpus (1)

• Shades of Hyperbolicity for Hamiltonians