Arnold diffusion in perturbations of analytic exact symplectic maps (Q1587218)

Arnold discovered in 1964 the diffusion in general perturbations of integrable systems. Douady proved in 1988 that Arnold diffusion can also be found in exact symplectic \(C^\infty\) maps. Now, the authors show that Arnold diffusion appears also in exact symplectic analytic maps. To prove this result they construct a family of exact symplectic analytic maps passing through certain integrable ones, and having a drift in the action variables of order 1 independent of the size of perturbation.