The Lyapunov exponents and the neighbourhood of periodic orbits
  We show that the Lyapunov exponents of a periodic orbit can be easily
obtained from the eigenvalues of the monodromy matrix. It turns out that the
Lyapunov exponents of simply stable periodic orbits are all zero, simply
unstable periodic orbits have only one positive Lyapunov exponent, doubly
unstable periodic orbits have two different positive Lyapunov exponents and the
two positive Lyapunov exponents of complex unstable periodic orbits are equal.
We present a numerical example for periodic orbits in a realistic galactic
potential. Moreover, the center manifold theorem allowed us to show that
stable, simply unstable and doubly unstable periodic orbits are the mothers of
families of, respectively, regular, partially and fully chaotic orbits in their
neighbourhood.
