José Pedro Gaivão
CEMAPRE and ISEG, Universidade de Lisboa

Abstract: In the 20’s Birkhoff proved that any invariant curve of a symplectic twist map of the annulus which is not homotopic to a point (essential curve) is the graph of a Lipschitz function. An open question of Mather asks for an example of a Cr symplectic twist map with an invariant essential curve that is not C1 and that contains no periodic point. In this talk we will discuss the construction of such example when r = 1. The example is due to Marie-Claude Arnaud. The cases r >1 and r = ω remain open.

This seminar is supported by National Funding from FCT - Fundação para a Ciência e a Tecnologia, under the project: UID/MAT/04561/2013.