Abstract
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.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
