Computation of bifurcation manifolds of linearly independent homoclinic orbits

DOI10.1016/j.jde.2008.06.029zbMath1160.34043OpenAlexW2000874527MaRDI QIDQ947147

Chang Rong Zhu, Wei Nian Zhang

Publication date: 29 September 2008

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2008.06.029

zbMATH Keywords

codimensionLyapunov-Schmidt reductionlinear independencedegenerate homoclinic bifurcationbifurcation manifold

Mathematics Subject Classification ID

Bifurcation theory for ordinary differential equations (34C23) Ordinary differential equations and systems on manifolds (34C40) Numerical bifurcation problems (65P30) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37)

Related Items (6)

Homoclinic finger-rings in \(\mathbb{R}^N\) ⋮ Existence of homoclinic solutions for nonlinear second-order problems ⋮ Multiple families of bounded solutions near perturbed homoclinic orbits, application to a nonlinear wave equation ⋮ Homoclinic solutions for a forced generalized Liénard system ⋮ Homoclinic solutions for a forced Liénard type system ⋮ Eventually vanishing solutions of a forced Liénard system

Cites Work

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• Perturbation of homoclinics and subharmonics in duffing's equation
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• Tangencies between stable and unstable manifolds
• Homoclinic Solutions for Autonomous Dynamical Systems in Arbitrary Dimension
• Homoclinic points near degenerate homoclinics
• Bounded solutions for non-autonomous parabolic equations

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