Arnaud, Marie-Claude; Bonatti, Christian; Crovisier, Sylvain Generic symplectic dynamics. (Dynamiques symplectiques génériques.) (French) Zbl 1084.37017 Ergodic Theory Dyn. Syst. 25, No. 5, 1401-1436 (2005). 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. Reviewer: Constantin Udrişte (Bucureşti) Cited in 2 ReviewsCited in 21 Documents 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 PDFBibTeX XMLCite \textit{M.-C. Arnaud} et al., Ergodic Theory Dyn. Syst. 25, No. 5, 1401--1436 (2005; Zbl 1084.37017) Full Text: DOI