Abstract

Our aim is to describe the “amount of nonhyperbolicity” either on an orbit-wise level or on a measure-wise one. This is done in the simplest setting of step skew products defined over a shift and with circle fiber maps, which provides a convenient model for partially hyperbolic diffeomorphisms with one-dimensional central bundle. Starting point is topologically transitive systems which display coexisting regions with different type of hyperbolicity. Transitivity forces an interaction between these regions and the emergence of nonhyperbolicity.We review three, closely related, main mechanisms to construct nonhyperbolic ergodic measures. One main approach is to ergodically approximate nonhyperbolicity by hyperbolicity.

Full Text
Paper version not known

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 call

Disclaimer: 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.