Bifurcation of a reversible Hamiltonian system from a fixed point with fourfold eigenvalue zero

DOI10.1080/14689360110089831zbMath1053.37032OpenAlexW1985354390MaRDI QIDQ4432897

Thomas Wagenknecht

Publication date: 2002

Published in: Dynamical Systems (Search for Journal in Brave)

Full work available at URL: http://eprints.maths.manchester.ac.uk/616/1/ds_02.pdf

zbMATH Keywords

Hamiltonian systemsnormal formsbifurcationsvector fieldsunfolding

Mathematics Subject Classification ID

Bifurcation problems for finite-dimensional Hamiltonian and Lagrangian systems (37J20) Bifurcation theory for ordinary differential equations (34C23) Normal forms for dynamical systems (37G05) Bifurcations of singular points in dynamical systems (37G10) Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion (37J40) Singularities of vector fields, topological aspects (58K45) Normal forms on manifolds (58K50) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37)

Related Items (2)

Heteroclinic solutions for a class of the second order Hamiltonian systems ⋮ Stability conditions for reversible and partially integrable systems

Cites Work

• Perturbed homoclinic solutions in reversible 1:1 resonance vector fields
• The reversible umbilic bifurcation
• Homoclinic orbits in reversible systems and their applications in mechanics, fluids and optics
• Homoclinic, heteroclinic, and periodic orbits for a class of indefinite Hamiltonian systems
• Generic bifurcation of Hamiltonian systems with symmetry. With an appendix by Jerrold Marsden
• Homoclinic period blow-up in reversible and conservative systems
• Singularites \(C^\infty\) en presence de symétrie. En particulier en presence de la symétrie d'un groupe de Lie compact
• A normally elliptic Hamiltonian bifurcation
• Homotopy classes for stable connections between Hamiltonian saddle-focus equilibria
• Singularity theory and equivariant symplectic maps
• Singularities of reversible vector fields
• Versal deformations and normal forms for reversible and Hamiltonian linear systems
• Bifurcation of a plethora of multi-modal homoclinic orbits for autonomous Hamiltonian systems
• Differential Topology
• Shooting methods and topological transversality
• Hopf bifurcation for equivariant conservative and time-reversible systems

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