4 research outputs found
Periodic orbits in the case of a zero eigenvalue
We will show that if a dynamical system has enough constants of motion then a
Moser-Weinstein type theorem can be applied for proving the existence of
periodic orbits in the case when the linearized system is degenerate.Comment: 6 pages, no figure
On the symmetry breaking phenomenon
We investigate the problem of symmetry breaking in the framework of dynamical
systems with symmetry on a smooth manifold. Two cases will be analyzed: general
and Hamiltonian dynamical systems. We give sufficient conditions for symmetry
breaking in both cases