On two-dimensional area-preserving maps with homoclinic tangencies that have infinitely many generic elliptic periodic points

DOI10.1007/s10958-005-0228-6zbMath1120.37041OpenAlexW1998639256MaRDI QIDQ997763

L. P. Shil'nikov, Sergey V. Gonchenko

Publication date: 7 August 2007

Published in: Journal of Mathematical Sciences (New York) (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10958-005-0228-6

zbMATH Keywords

symplectic diffeomorphismssemilocal dynamics

Mathematics Subject Classification ID

Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion (37J40) Fixed points and periodic points of dynamical systems; fixed-point index theory; local dynamics (37C25) Homoclinic and heteroclinic orbits for dynamical systems (37C29) Bifurcations connected with nontransversal intersection in dynamical systems (37G25)

Related Items (7)

Unfolding globally resonant homoclinic tangencies ⋮ On bifurcations of area-preserving and nonorientable maps with quadratic homoclinic tangencies ⋮ On Bifurcations of Homoclinic Tangencies in Area-Preserving Maps on Non-orientable Manifolds ⋮ Subsumed Homoclinic Connections and Infinitely Many Coexisting Attractors in Piecewise-Linear Maps ⋮ Homoclinic tangencies with infinitely many asymptotically stable single-round periodic solutions ⋮ Unfolding Codimension-Two Subsumed Homoclinic Connections in Two-Dimensional Piecewise-Linear Maps ⋮ Robust cycles unfolding from conservative bifocal homoclinic orbits

Cites Work

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• Invariants of \(\Omega\)-conjugacy of diffeomorphisms with a nongeneric homoclinic trajectory
• Arithmetic properties of topological invariants of systems with nonstructurally stable homoclinic trajectories
• On two-dimensional area-preserving mappings with homoclinic tangencies.
• The analytic invariants of an area-preserving mapping near a hyperbolic fixed point
• ON MODULI OF SYSTEMS WITH A STRUCTURALLY UNSTABLE HOMOCLINIC POINCARÉ CURVE
• ON GEOMETRICAL PROPERTIES OF TWO-DIMENSIONAL DIFFEOMORPHISMS WITH HOMOCLINIC TANGENCIES
• ON THREE-DIMENSIONAL DYNAMICAL SYSTEMS CLOSE TO SYSTEMS WITH A STRUCTURALLY UNSTABLE HOMOCLINIC CURVE. I
• On two-dimensional area-preserving diffeomorphisms with infinitely many elliptic islands

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