Bifurcation of Homoclinic Orbits to a Saddle-Center in Reversible Systems

DOI10.1142/S0218127403008119zbMath1052.37043MaRDI QIDQ3046556

Jürgen Knobloch, Joachim Klaus

Publication date: 12 August 2004

Published in: International Journal of Bifurcation and Chaos (Search for Journal in Brave)

zbMATH Keywords

homoclinic solutionssmall perturbationsnonhyperbolic equilibriumLyapunov center theorembifurcation studytime-reversible systems

Mathematics Subject Classification ID

Homoclinic and heteroclinic orbits for dynamical systems (37C29) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37) Hyperbolic singular points with homoclinic trajectories in dynamical systems (37G20)

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Cites Work

• Heteroclinic orbits for retarded functional differential equations
• Cascades of homoclinic orbits to, and chaos near, a Hamiltonian saddle- center
• Bifurcation of degenerate homoclinics
• Homoclinic period blow-up in reversible and conservative systems
• Bifurcation of degenerate homoclinic orbits in reversible and conservative systems
• Using Melnikov's method to solve Silnikov's problems
• FAMILIES OF TRANSVERSE POINCARÉ HOMOCLINIC ORBITS IN 2N-DIMENSIONAL HAMILTONIAN SYSTEMS CLOSE TO THE SYSTEM WITH A LOOP TO A SADDLE-CENTER
• PERIODIC AND HOMOCLINIC ORBITS IN A TWO-PARAMETER UNFOLDING OF A HAMILTONIAN SYSTEM WITH A HOMOCLINIC ORBIT TO A SADDLE-CENTER
• Cascades of homoclinic orbits to a saddle-centre for reversible and perturbed Hamiltonian systems