Symmetric Liapunov center theorem for orbit with nontrivial isotropy group

2018/10/22 by Kowalczyk, Marta, Pérez-Chavela, Ernesto, Rybicki, Sławomir
#Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.1810.09293

Abstract

In this article we prove two versions of the Liapunov center theorem for symmetric potentials. We consider a~second order autonomous system q(t)=-∇ U(q(t)) in the presence of symmetries of a compact Lie group Γ acting linearly on ℝⁿ. We look for non-stationary periodic solutions of this system in a~neighborhood of an orbit of critical points of the potential U.

Related

• Symmetric Liapunov center theorem for minimal orbit
• Periodic solutions to symmetric Newtonian systems in neighborhoods of orbits of equilibria
• Patterns of Non-Stationary Solutions to Symmetric Systems of Second-Order Differential Equations
• Centers with equal period functions
• Periodic orbits in Hamiltonian systems with involutory symmetries