  This paper deals with the dynamics of time-reversible Hamiltonian vector
fields with 2 and 3 degrees of freedom around an elliptic equilibrium point in
presence of symplectic involutions. The main results discuss the existence of
one-parameter families of reversible periodic solutions terminating at the
equilibrium. The main techniques used are Birkhoff and Belitskii normal forms
combined with the Liapunov-Schmidt reduction.
