On two-dimensional area-preserving mappings with homoclinic tangencies.

zbMath1041.37033MaRDI QIDQ1432575

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

Publication date: 15 June 2004

Published in: Doklady Mathematics (Search for Journal in Brave)

zbMATH Keywords

homoclinic orbitstructure of the set of trajectoriestwo-dimensional area-preserving mapping

Mathematics Subject Classification ID

Fixed points and periodic points of dynamical systems; fixed-point index theory; local dynamics (37C25) Dynamical systems with hyperbolic orbits and sets (37D05) Infinite nonwandering sets arising in bifurcations of dynamical systems (37G30) Bifurcations connected with nontransversal intersection in dynamical systems (37G25)

Related Items (10)

Mixed dynamics of 2-dimensional reversible maps with a symmetric couple of quadratic homoclinic tangencies ⋮ On a homoclinic origin of Hénon-like maps ⋮ 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 ⋮ Steady Euler flows on \({\mathbb{R}}^3\) with wild and universal dynamics ⋮ On mixed dynamics of two-dimensional reversible diffeomorphisms with symmetric non-transversal heteroclinic cycles ⋮ On cascades of elliptic periodic points in two-dimensional symplectic maps with homoclinic tangencies ⋮ From the Hénon conservative map to the Chirikov standard map for large parameter values ⋮ On two-dimensional area-preserving maps with homoclinic tangencies that have infinitely many generic elliptic periodic points ⋮ Effect of islands in diffusive properties of the standard map for large parameter values

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