# Actions of symplectic homeomorphisms/diffeomorphisms on foliations by curves in dimension 2

```@article{Arnaud2020ActionsOS,
title={Actions of symplectic homeomorphisms/diffeomorphisms on foliations by curves in dimension 2},
author={Marie-Claude Arnaud and Maxime Zavidovique},
journal={Ergodic Theory and Dynamical Systems},
year={2020}
}```
• Published 2 November 2020
• Mathematics
• Ergodic Theory and Dynamical Systems
The two main results in this paper concern the regularity of the invariant foliation of a \$C^0\$ -integrable symplectic twist diffeomorphism of the two-dimensional annulus, namely that (i) the generating function of such a foliation is \$C^1\$ , and (ii) the foliation is Hölder with exponent \$\tfrac 12\$ . We also characterize foliations by graphs that are straightenable via a symplectic homeomorphism and prove that every symplectic homeomorphism that leaves invariant…
1 Citations
• Mathematics
• 2022
. For exact symplectic twist maps of the annulus, we etablish a choice of weak K.A.M. solutions u c = u ( · ,c ) that depend in a Lipschitz-continuous way on the cohomology class c . This allows us

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