On two-dimensional area-preserving maps with homoclinic tangencies that have infinitely many generic elliptic periodic points. (English. Russian original) Zbl 1120.37041

Gonchenko, S. V.; Shil’nikov, L. P.

J. Math. Sci., New York 128, No. 2, 2767-2773 (2005); translation from Zap. Nauchn. Semin. POMI 300, 155-166 (2003).

Summary: We study the semilocal dynamics of two-dimensional symplectic diffeomorphisms with homoclinic tangencies. Conditions for the existence of infinitely many generic elliptic periodic orbits of successive periods starting with some integer are found.

MSC:

37J45	Periodic, homoclinic and heteroclinic orbits; variational methods, degree-theoretic methods (MSC2010)
37J40	Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol’d diffusion
37J10	Symplectic mappings, fixed points (dynamical systems) (MSC2010)
37C29	Homoclinic and heteroclinic orbits for dynamical systems
37C25	Fixed points and periodic points of dynamical systems; fixed-point index theory; local dynamics
37G25	Bifurcations connected with nontransversal intersection in dynamical systems

Keywords:

semilocal dynamics; symplectic diffeomorphisms

References:

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