Bifurcations of twisted homoclinic loops for degenerated cases

DOI10.1007/s11766-003-0023-4zbMath1027.37032OpenAlexW115947493MaRDI QIDQ1413702

Yin Lai Jin

Publication date: 17 November 2003

Published in: Applied Mathematics. Series B (English Edition) (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11766-003-0023-4

zbMATH Keywords

local coordinatesbifurcation problemstwisted and degenerated homoclinic loops

Mathematics Subject Classification ID

Bifurcation theory for ordinary differential equations (34C23) Bifurcations of limit cycles and periodic orbits in dynamical systems (37G15) Homoclinic and heteroclinic orbits for dynamical systems (37C29) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37)

Cites Work

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• Homoclinic bifurcation at resonant eigenvalues
• The Sil'nikov problem, exponential expansion, strong \(\lambda\)-lemma, \(C^ 1\)-linearization, and homoclinic bifurcation
• Degenerated homoclinic bifurcations with higher dimensions
• Problems in homoclinic bifurcation with higher dimensions
• Bifurcation Theory and Methods of Dynamical Systems
• Exponential trichotomy and heteroclinic bifurcations