2 problems

Let $(S,\Omega)$ be an analytic closed symplectic surface, and let $f\in \operatorname{Diff}^{\omega}_{\Omega}(S)$ be an analytic symplectic diffeomorphism displaying an elliptic p…

Let the disk carry its standard analytic symplectic structure, and let an analytic symplectic perturbation of the identity mean an analytic symplectic diffeomorphism sufficiently c…