Abstract
We discuss several symplectic aspects related to the Mane critical value cu of the universal cover of a Tonelli Hamiltonian. In particular we show that the critical energy level is never of virtual contact type for manifolds of dimension greater than or equal to three. We also show the symplectic invariance of the finiteness of the Peierls barrier and the Aubry set of the universal cover. We also provide an example where cu coincides with the infimum of Mather’s α function but the Aubry set of the universal cover is empty and the Peierls barrier is finite. A second example exhibits all the ergodic invariant minimizing measures with zero homotopy, showing, quite surprinsingly, that the union of their supports is not a graph, in contrast with Mather’s celebrated graph theorem.
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 callMore From: Nonlinear Differential Equations and Applications NoDEA
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.
