This is a (probably very naive question) about area-preserving maps of surfaces.
Does there exist a Hamiltonian diffeomorphism $$ f: \Sigma \to \Sigma $$ of a symplectic surface (real dimension $2$), possibly with boundary $\partial \Sigma$, such that $f|_{\partial \Sigma} = id$, and such that all periodic points of $f$ in the interior of $\Sigma$ are hyperbolic in the sense if $x$ is a periodic point, i.e. $f^n(x) = x$, then $d(f^n): T_x\Sigma \to T_x\Sigma$ has no eigenvalues on the unit circle?
If one exists, what is a simple construction of such an $f$?
