  We study the dynamics of the space debris in the 1:1 and 2:1 resonances,
where geosynchronous and GPS satellites are located. By using Hamiltonian
formalism, we consider a model including the geopotential contribution for
which we compute the secular and resonant expansions of the Hamiltonian.
  Within such model we are able to detect the equilibria and to study the main
features of the resonances in a very effective way. In particular, we analyze
the regular and chaotic behavior of the 1:1 and 2:1 resonant regions by
analytical methods and by computing the Fast Lyapunov Indicators, which provide
a cartography of the resonances. This approach allows us to detect easily the
location of the equilibria, the amplitudes of the libration islands and the
main dynamical stability features of the resonances, thus providing an overview
of the 1:1 and 2:1 resonant domains under the effect of Earth's oblateness.
  The results are validated by a comparison with a model developed in Cartesian
coordinates, including the geopotential, the gravitational attraction of Sun
and Moon and the solar radiation pressure.
