Abstract
We consider the irrational Aubry-Mather sets of an exact symplectic monotone C 1 twist map of the two-dimensional annulus, introduce for them a notion of \C 1 -regularity (related to the notion of Bouligand paratingent cone) and prove that a Mather measure has zero Lyapunov exponents if and only if its support is C 1 -regular almost everywhere; a Mather measure has nonzero Lyapunov exponents if and only if its support is C 1 -irregular almost everywhere; an Aubry-Mather set is uniformly hyperbolic if and only if it is everywhere; the Aubry-Mather sets which are close to the KAM invariant curves, even if they may be C 1 -irregular, are not \too irregular (i.e., have small paratingent cones). The main tools that we use in the proofs are the so-called Green bundles.
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.
