Partial hyperbolicity and pseudo orbit tracing properties.

It is known that if a closed invariant set Λ of a diffeomorphism f of a compact smooth manifold M is hyperbolic then f has the pseudo orbit tracing property. For a weak notion of hyperbolicity, in [4] if a transitive set of a diffeomorphism f of the three dimensional manifold M has a partially hyperbolic structure then f does not have the pseudo orbit tracing property. From the results, we consider a compact smooth manifold M which the dimension is greater than three. It is a general version of the three dimensional manifold M. More detail, we show that if a transitive diffeomorphism f of a compact smooth manifold M is partially hyperbolic, then f does not have the pseudo orbit tracing property. Moreover, if f is partially hyperbolic on M then f does not have the asymtotic and the ergodic pseudo orbit tracing properties. [ABSTRACT FROM AUTHOR]