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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
##### Keywords:
perturbations; symplectic diffeomorphisms; periodic orbits
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