Stability and persistence of relative equilibria at singular values of the moment map

DOI10.1088/0951-7715/11/6/012zbMath0927.37032OpenAlexW1972991444MaRDI QIDQ4223741

Eugene Lerman, Stephanie Frank Singer

Publication date: 11 March 1999

Published in: Nonlinearity (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1088/0951-7715/11/6/012

zbMATH Keywords

stabilityrelative equilibriasingular pointspersistencemomentum mapsymmetric Hamiltonian systems

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Stability problems for finite-dimensional Hamiltonian and Lagrangian systems (37J25)

Related Items

Nonlinear stability of Riemann ellipsoids with symmetric configurations ⋮ Point vortices on the hyperbolic plane ⋮ A cotangent bundle slice theorem ⋮ Bifurcation of relative equilibria in mechanical systems with symmetry ⋮ A Dirichlet criterion for the stability of periodic and relative periodic orbits in Hamiltonian systems ⋮ Nonlinear stability of singular relative periodic orbits in Hamiltonian systems with symmetry ⋮ Continuous singularities in Hamiltonian relative equilibria with abelian momentum isotropy ⋮ The symplectic normal space of a cotangent-lifted action ⋮ Nonlinear stability of relative equilibria and isomorphic vector fields ⋮ Orbital stability via the energy-momentum method: the case of higher dimensional symmetry groups ⋮ Asymptotic and Lyapunov stability of constrained and Poisson equilibria ⋮ Persistence of stationary motion under explicit symmetry breaking perturbation ⋮ Stability of Poisson equilibria and Hamiltonian relative equilibria by energy methods ⋮ Relative equilibria in systems with configuration space isotropy ⋮ Symplectic slice for subgroup actions ⋮ Bifurcations of relative equilibria near zero momentum in Hamiltonian systems with spherical symmetry ⋮ Stability of Hamiltonian relative equilibria in symmetric magnetically confined rigid bodies ⋮ Orbital Stability: Analysis Meets Geometry ⋮ Hamiltonian systems near relative equilibria