Hamiltonian Relative Equilibria with Continuous Isotropy

2015/09/16 by James Montaldi, Montaldi, James, Miguel Rodríguez-Olmos +1 · 1 citation
Materials Science · Physics and Astronomy · #37J20 #70H33 #Advanced Thermodynamics and Statistical Mechanics #Dynamical Systems (math.DS) #FOS: Mathematics #Magnetism in coordination complexes #Quantum chaos and dynamical systems

paper · doi:10.48550/arxiv.1509.04961

openalex publication_date 2015/09/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In symmetric Hamiltonian systems, relative equilibria usually arise in continuous families. The geometry of these families in the setting of free actions of the symmetry group is well-understood. Here we consider the question for non-free actions. Some results are already known in this direction, and we use the so called bundle equations to provide a systematic treatment of this question which both consolidates the known results, extending the scope of the results to deal with non-compact symmetry groups, as well as producing new results. Specifically we address questions about the stability, persistence and bifurcations of these relative equilibria.

Cited by

• The Lagrange-Poincaré equations for a mechanical system with symmetry on the principal fiber bundle over the base represented by the bundle space of the associated bundle
• The Fast-Superfast Transition in the Sleeping Lagrange Top

Related

• Bifurcation of relative equilibria in mechanical systems with symmetry
• Bifurcation and forced symmetry breaking in Hamiltonian systems
• The dynamics around stable and unstable Hamiltonian relative equilibria
• G-isotropy of T-relative equilibria within manifolds tangent to spaces with linearly independent weights
• Openness of momentum maps and persistence of extremal relative equilibria