Boundaries of instability zones for symplectic twist maps

Marie-Claude Arnaud (1)

1 LMA - EA2151 Laboratoire de Mathématiques d'Avignon

We construct a C^2 symplectic twist map f of the annulus that has an essential invariant curve C such that: -C is not differentiable; - the dynamics of f restricted to C is conjugated to the one of a Denjoy counter-example; -C is at the boundary of an instability zone for f.

Keywords: twist maps; invariant curves; instability zones; Denjoy counter-example

Domains: Dynamical Systems [math.DS]

Marie-Claude Arnaud. Boundaries of instability zones for symplectic twist maps. J. Inst. Math. Jussieu, 2014, 13 (1), pp.19-41. ⟨hal-00691483⟩