  Using bifurcation theory, we study the secular resonances induced by the Sun
and Moon on space debris orbits around the Earth. In particular, we concentrate
on a special class of secular resonances, which depend only on the debris'
orbital inclination. This class is typically subdivided into three distinct
types of secular resonances: those occurring at the critical inclination, those
corresponding to polar orbits, and a third type resulting from a linear
combination of the rates of variation of the argument of perigee and the
longitude of the ascending node.
  The model describing the dynamics of space debris includes the effects of the
geopotential, as well as the Sun's and Moon's attractions, and it is defined in
terms of suitable action-angle variables. We consider the system averaged over
both the mean anomaly of the debris and those of the Sun and Moon. Such
multiply-averaged Hamiltonian is used to study the lunisolar resonances which
depend just on the inclination.
  Borrowing the technique from the theory of bifurcations of Hamiltonian normal
forms, we study the birth of periodic orbits and we determine the energy
thresholds at which the bifurcations of lunisolar secular resonances take
place. This approach gives us physically relevant information on the existence
and location of the equilibria, which help us to identify stable and unstable
regions in the phase space. Besides their physical interest, the study of
inclination dependent resonances offers interesting insights from the dynamical
point of view, since it sheds light on different phenomena related to
bifurcation theory.
