Generic expansive symplectic diffeomorphisms (Q2927686)

Symplectic maps are the maps on a symplectic manifold \((M,\omega)\) that preserve the symplectic form \(\omega\). This class of maps enjoy many desirable properties. A classical result of \textit{S. E. Newhouse} [Am. J. Math. 99, 1061--1087 (1977; Zbl 0379.58011)] states that a generic symplectic map is either Anosov, or the set of quasi-periodic points is dense on \(M\).NEWLINENEWLINEIn this paper, the author considers a generic symplectic map that is expansive. Clearly an Anosov map is expansive. On the other hand, the existence of quasi-elliptic periodic points is an obstruction to expansiveness. The author shows that a generic expansive symplectic diffeomorphism is mixing Anosov.