  We study the dynamics of the space debris in regions corresponding to minor
resonances; precisely, we consider the resonances 3:1, 3:2, 4:1, 4:3, 5:1, 5:2,
5:3, 5:4, where a j:l resonance (with j, l integers) means that the periods of
revolution of the debris and of rotation of the Earth are in the ratio j/l. We
consider a Hamiltonian function describing the effect of the geopotential and
we use suitable finite expansions of the Hamiltonian for the description of the
different resonances. In particular, we determine the leading terms which
dominate in a specific orbital region, thus limiting our computation to very
few harmonics. Taking advantage from the pendulum-like structure associated to
each term of the expansion, we are able to determine the amplitude of the
islands corresponding to the different harmonics. By means of simple
mathematical formulae, we can predict the occurrence of splitting or
overlapping of the resonant islands for different values of the parameters. We
also find several cases which exhibit a transcritical bifurcation as the
inclination is varied. These results, which are based on a careful mathematical
analysis of the Hamiltonian expansion, are confirmed by a numerical study of
the dynamical behavior obtained by computing the so-called Fast Laypunov
Indicators. Since the Hamiltonian approach includes just the effect of the
geopotential, we validate our results by performing a numerical integration in
Cartesian variables of a more complete model including the gravitational
attraction of Sun and Moon, as well as the solar radiation pressure.
