Invariant manifolds in the Hamiltonian-Hopf bifurcation

DOI10.1007/S12346-020-00376-3zbMath1439.37052OpenAlexW2970089786MaRDI QIDQ2301840

Kenneth R. Meyer, Dieter S. Schmidt

Publication date: 25 February 2020

Published in: Qualitative Theory of Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s12346-020-00376-3

zbMATH Keywords

bifurcationrestricted three-body problemstable manifoldSmale horseshoe

Mathematics Subject Classification ID

Bifurcation problems for finite-dimensional Hamiltonian and Lagrangian systems (37J20) Three-body problems (70F07) Bifurcation theory for ordinary differential equations (34C23) Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion (37J40) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37) Stability problems for finite-dimensional Hamiltonian and Lagrangian systems (37J25) Periodic, homoclinic and heteroclinic orbits of finite-dimensional Hamiltonian systems (37J46)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Analytic invariants for the \(1 : - 1\) resonance
• Perturbed homoclinic solutions in reversible 1:1 resonance vector fields
• Stability of a Hamiltonian system in a limiting case
• The evolution of invariant manifolds in Hamiltonian-Hopf bifurcations
• Splitting of separatrices for the Hamiltonian-Hopf bifurcation with the Swift–Hohenberg equation as an example
• Hopf bifurcation with non-semisimple 1:1 resonance
• Periodic orbits near ?4 for mass ratios near the critical mass ratio of routh
• Probleme General de la Stabilite du Mouvement. (AM-17)
• Introduction to Hamiltonian dynamical systems and the \(N\)-body problem

This page was built for publication: Invariant manifolds in the Hamiltonian-Hopf bifurcation