A remark on papers by pixton and oliveira: Genericity of symplectic diffeomorphisms ofS 2 with positive topological entropy

We prove the existence of an open and dense subset of mapsfeDiff ω ∞ (S2) which have positive topological entropy. It follows that these maps have infinitely many hyperbolic periodic points and an exponential growth rate of hyperbolic periodic points. The proof is an application of Pixton's theorem