Exponential trichotomy and homoclinic bifurcation with saddle-center equilibrium

DOI10.1016/j.aml.2009.11.008zbMath1210.34062OpenAlexW2030448853MaRDI QIDQ963821

Xing Bo Liu

Publication date: 14 April 2010

Published in: Applied Mathematics Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.aml.2009.11.008

zbMATH Keywords

Liapunov-Schmidt methodexponential trichotomies

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Singular perturbations, turning point theory, WKB methods for ordinary differential equations (34E20) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37) Dichotomy, trichotomy of solutions to ordinary differential equations (34D09)

Related Items (2)

Discrete admissibility and exponential trichotomy of dynamical systems ⋮ Lyapunov function and exponential trichotomy on time scales

Cites Work

• Homoclinic bifurcation with nonhyperbolic equilibria
• Exponential trichotomy, orthogonality condition and their application
• Bifurcation from homoclinic to periodic solutions in singular ordinary differential equations
• Saddle-node bifurcation of homoclinic orbits in singular systems
• Homoclinic solutions for autonomous ordinary differential equations with nonautonomous perturbations
• Singular heteroclinic cycles
• Detection of symmetric homoclinic orbits to saddle-centres in reversible systems
• Bifurcations of invariant tori and subharmonic solutions of singularly perturbed system
• Homoclinic Bifurcations with Nonhyperbolic Equilibria
• The coexistence of subharmonics bifurcated from homoclinic orbits in singular systems
• Unnamed Item

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