Homoclinic finger-rings in \(\mathbb{R}^N\)

DOI10.1016/j.jde.2017.04.026zbMath1442.34080OpenAlexW2612845992MaRDI QIDQ2358276

Wei Nian Zhang, Chang Rong Zhu

Publication date: 14 June 2017

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

Full work available at URL: https://doi.org/10.1016/j.jde.2017.04.026

zbMATH Keywords

widthdegenerate homoclinic orbitbifurcation manifoldhomoclinic finger-ring

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Bifurcation theory for ordinary differential equations (34C23) Invariant manifolds for ordinary differential equations (34C45) Computational methods for bifurcation problems in dynamical systems (37M20) Homoclinic and heteroclinic orbits for dynamical systems (37C29) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37) Dichotomy, trichotomy of solutions to ordinary differential equations (34D09)

Related Items (3)

Families of bounded solutions near perturbed homoclinics of R.D.E.s with symmetric eigenvalues, application to retarded power-law oscillations ⋮ Multiple families of bounded solutions near perturbed homoclinic orbits, application to a nonlinear wave equation ⋮ Multiple chaos arising from single-parametric perturbation of a degenerate homoclinic orbit

Cites Work

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• Computation of bifurcation manifolds of linearly independent homoclinic orbits
• Linearly independent homoclinic bifurcations parameterized by a small function
• Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
• An example of bifurcation to homoclinic orbits
• Manifolds, tensor analysis, and applications.
• Bifurcation of degenerate homoclinic orbits in reversible and conservative systems
• Bifurcation from degenerate homoclinics in periodically forced systems
• Subharmonic bifurcations in a perturbed nonlinear oscillation
• Exponential dichotomies and transversal homoclinic points
• Homoclinic solutions for autonomous ordinary differential equations with nonautonomous perturbations
• Exponential dichotomies and transversal homoclinic orbits in degenerate cases
• Existence of transversal homoclinic points in a degenerate case
• Bifurcation of homoclinics in a nonlinear oscillation
• Perturbation of homoclinics and subharmonics in duffing's equation
• Homoclinic Solutions for Autonomous Dynamical Systems in Arbitrary Dimension

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