Abstract:
A general method is presented for constructing a nonlinear canonical transformation,
which makes it possible to introduce local variables in a neighborhood of periodic motions
of an autonomous Hamiltonian system with two degrees of freedom. This method can be used for
investigating the behavior of the Hamiltonian system in the vicinity of its periodic trajectories.
In particular, it can be applied to solve the problem of orbital stability of periodic motions.
Keywords:normal form, KAM theory, orbital stability, periodic orbit, Hamiltonian system, canonical transformation.
References