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Generic symplectic dynamics. (Dynamiques symplectiques génériques.) (French) Zbl 1084.37017
The authors prove that \(C^1\)-generic symplectic diffeomorphisms of a compact manifold are transitive and that the generic orbits of generic diffeomorphisms on noncompact manifolds are not bounded. The main tool is a connecting lemma for pseudo-orbits of symplectic diffeomorphisms.

MSC:
37C05 Dynamical systems involving smooth mappings and diffeomorphisms
37C20 Generic properties, structural stability of dynamical systems
53D35 Global theory of symplectic and contact manifolds
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