Special Session 105: 

Various shadowing properties for partial hyperbolicity

Manseob Lee
Mokwon University
Korea
Co-Author(s):    Jiweon Ahn
Abstract:
Let $f:M\to M$ be a diffeomorphism on $C^{\infty}$ manifold $M^d(d\geq 3).$ If $f$ is transitive with a partially hyperbolic splitting on $M$, then $f$ does not have the shadowing property. Moreover, if $f$ admits a partially hyperbolic splitting on $M$ then $f$ does not have the limit shadowing and the ergodic shadowing properties.