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MR1944396 37J10 (37C05 37C20 37C25 37D30)
Arnaud, Marie-Claude The generic symplectic $C^1$-diffeomorphisms of four-dimensional symplectic manifolds are hyperbolic, partially hyperbolic or have a completely elliptic periodic point. Ergodic Theory Dynam. Systems 22 (2002), no. 6, 1621–1639.
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