Torsion of instability zones for conservative twist maps on the annulus

2020/06/08 by Florio, Anna, Calvez, Patrice Le
#Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.2006.04447

Abstract

For a twist map f of the annulus preserving the Lebesgue measure, we give sufficient conditions to assure the existence of a set of positive measure of points with non-zero asymptotic torsion. In particular, we deduce that every bounded instability region for f contains a set of positive measure of points with non-zero asymptotic torsion. Moreover, for an exact symplectic twist map f, we provide a simple, geometric proof of a result by Cheng and Sun (see [CS96]) which characterizes C⁰-integrability of f by the absence of conjugate points.

Related

• Boundaries of instability zones for symplectic twist maps
• Regions of instability for non-twist maps
• The C⁰ integrability of symplectic twist maps without conjugate points
• On the fragility of periodic tori for families of symplectic twist maps
• Rotation Numbers and Instability Sets