Gonchenko, S. V.; Shilnikov, L. P. On two-dimensional area-preserving diffeomorphisms with infinitely many elliptic islands. (English) Zbl 0987.37062 J. Stat. Phys. 101, No. 1-2, 321-356 (2000). The authors prove existence of \(C^r\)-smooth \((r\geq 6)\) area-preserving symplectic diffeomorphisms which have, in a bounded domain of the phase space, infinitely many isolated generic elliptic periodic points and, as a result, infinitely many elliptic islands. Note that they study two parameter families of maps, that are diffeomorphisms with simplest structurally unstable heteroclinic cycles. Reviewer: Messoud Efendiev (Berlin) Cited in 15 Documents MSC: 37J45 Periodic, homoclinic and heteroclinic orbits; variational methods, degree-theoretic methods (MSC2010) 37C25 Fixed points and periodic points of dynamical systems; fixed-point index theory; local dynamics 37G25 Bifurcations connected with nontransversal intersection in dynamical systems 37C29 Homoclinic and heteroclinic orbits for dynamical systems 37J10 Symplectic mappings, fixed points (dynamical systems) (MSC2010) Keywords:area-preserving symplectic diffeomorphisms; elliptic periodic points; elliptic islands; unstable heteroclinic cycles × Cite Format Result Cite Review PDF Full Text: DOI