Gonchenko, S. V.; Shil’nikov, L. P. On two-dimensional analytical area-preserving diffeomorphisms with a countable set of elliptic periodic points of stable type. (Russian. English summary) Zbl 1083.37524 Regul. Khaoticheskaya Din. 2, No. 3-4, 106-123 (1997). 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. Cited in 6 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 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) × Cite Format Result Cite Review PDF