| 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. |
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