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On two-dimensional area-preserving diffeomorphisms with infinitely many elliptic islands. (English) Zbl 0987.37062

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.

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)
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