Elliptic periodic orbits near a homoclinic tangency in four-dimensional symplectic maps and Hamiltonian systems with three degrees of freedom

DOI10.1070/rd1998v003n04ABEH000089zbMath0956.37048OpenAlexW4236119651MaRDI QIDQ1302428

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

Publication date: 31 March 2000

Published in: Regular and Chaotic Dynamics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1070/rd1998v003n04abeh000089

zbMATH Keywords

bifurcationsHénon mapsymplectic mapsaddle-focushomoclinic tangencyelliptic periodic orbit

Mathematics Subject Classification ID

Related Items (10)

Spiral chaos in the nonholonomic model of a Chaplygin top ⋮ 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 ⋮ Dynamical phenomena occurring due to phase volume compression in nonholonomic model of the rattleback ⋮ Steady Euler flows on \({\mathbb{R}}^3\) with wild and universal dynamics ⋮ On cascades of elliptic periodic points in two-dimensional symplectic maps with homoclinic tangencies ⋮ Hyperbolic properties of four-dimensional symplectic mappings with a structurally unstable trajectory homoclinic to a fixed point of the saddle-focus type ⋮ On symplectic dynamics near a homoclinic orbit to 1-elliptic fixed point ⋮ Stability in high dimensional steep repelling potentials

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