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

DOI10.1017/S0305004100069462zbMath0722.58032OpenAlexW2075079806MaRDI QIDQ3209906

Thomas J. Bridges

Publication date: 1990

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

Full work available at URL: https://doi.org/10.1017/s0305004100069462

zbMATH Keywords

Lyapunov-Schmidt methodKrein signaturecollision of eigenvalues

Mathematics Subject Classification ID

Three-body problems (70F07) Local and nonlocal bifurcation theory for dynamical systems (37G99)

Related Items (12)

Hamiltonian spatial structure for three-dimensional water waves in a moving frame of reference ⋮ Periodic traveling waves in diatomic granular chains ⋮ The Liapunov center theorem for a class of equivariant Hamiltonian systems ⋮ A transverse spinning double pendulum ⋮ Hamiltonian bifurcations of the spatial structure for coupled nonlinear Schrödinger equations ⋮ Poisson structure of the reversible \(1:1\) resonance ⋮ Resonant collisions in four-dimensional reversible maps: a description of scenarios ⋮ Bifurcations and monodromy of the axially symmetric \(1:1:-2\) resonance ⋮ Standing waves in a nonlinear 1D lattice: Floquet multipliers, Krein signatures, and stability ⋮ Algebraic methods for determining Hamiltonian Hopf bifurcations in three-degree-of-freedom systems ⋮ Instability and bifurcation near the symplectic 1 :4 resonance ⋮ Stability and Hamiltonian Hopf bifurcation for a nonlinear symmetric bladed rotor

Cites Work

• The Hamiltonian Hopf bifurcation
• Singularities and groups in bifurcation theory. Volume I
• Singularities and groups in bifurcation theory. Volume II
• On the stability of an autonomous Hamiltonian system with two degrees of freedom in the case of equal frequencies
• Foundations of the theory of 𝜆-zones of stability of a canonical system of linear differential equations with periodic coefficients
• Calculus of variations in the large and classical mechanics
• Linear stability of symplectic maps
• Strong Internal Resonance, $Z_2 \oplus Z_2 $ Symmetry, and Multiple Periodic Solutions
• Nonsemisimple 1?1 resonance at an equilibrium
• Versal deformations of linear Hamiltonian systems
• Normal forms for real linear Hamiltonian systems with purely imaginary eigenvalues
• Periodic orbits near ?4 for mass ratios near the critical mass ratio of routh

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