Communications of the
Korean Mathematical Society CKMS

Let $M$ be a closed, symplectic connected Riemannian manifold and $f$ a symplectomorphism on $M$. We prove that if $f$ is $C^1$-stably weak shadowable on $M$, then the whole manifold $M$ admits a partially hyperbolic splitting.

Keywords: partial hyperbolicity, weak shadowing, symplectomorphisms

MSC numbers: Primary 37D30, 37C50; Secondary 37J10