Stability of periodic solutions near a collision of eigenvalues of opposite signature

DOI10.1017/S0305004100069838zbMath0731.58028OpenAlexW2087721565MaRDI QIDQ3357138

Thomas J. Bridges

Publication date: 1991

Published in: Mathematical Proceedings of the Cambridge Philosophical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s0305004100069838

zbMATH Keywords

stabilityperiodic solutionsHamiltonian systems

Mathematics Subject Classification ID

Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems (37J99) Stability theory for smooth dynamical systems (37C75) Local and nonlocal bifurcation theory for dynamical systems (37G99)

Related Items

Geometric Aspects of Degenerate Modulation Equations ⋮ Krein's formula for indefinite multipliers in linear periodic Hamiltonian systems ⋮ Hamiltonian bifurcations of the spatial structure for coupled nonlinear Schrödinger equations ⋮ Poisson structure of the reversible \(1:1\) resonance ⋮ Stability of invariant curves in four-dimensional reversible mappings near 1:1 resonance ⋮ Bifurcations and monodromy of the axially symmetric \(1:1:-2\) resonance ⋮ Standing waves in a nonlinear 1D lattice: Floquet multipliers, Krein signatures, and stability

Cites Work

• The Hamiltonian Hopf bifurcation
• Singularities and groups in bifurcation theory. Volume I
• On the stability of an autonomous Hamiltonian system with two degrees of freedom in the case of equal frequencies
• Nonsemisimple 1?1 resonance at an equilibrium
• Reappraisal of the Kelvin–Helmholtz problem. Part 1. Hamiltonian structure
• Periodic orbits near ?4 for mass ratios near the critical mass ratio of routh