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On two-dimensional analytical area-preserving diffeomorphisms with a countable set of elliptic periodic points of stable type. (Russian. English summary) Zbl 1083.37524

Summary: We consider two-dimensional analitical area-preserving diffeomorphisms that have structurally unstable symplest heteroclinic cycles. We find the conditions when diffeomorphisms under consideration possess a countable set of periodic elliptic points of stable type.

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
37D05 Dynamical systems with hyperbolic orbits and sets
37E30 Dynamical systems involving homeomorphisms and diffeomorphisms of planes and surfaces
37J10 Symplectic mappings, fixed points (dynamical systems) (MSC2010)