  The motion of a satellite can experience secular resonances between the
precession frequencies of its orbit and the mean motion of the host planet
around the star. Some of these resonances can significantly modify the
eccentricity (evection resonance) and the inclination (eviction resonance) of
the satellite. In this paper, we study in detail the secular resonances that
can disturb the orbit of a satellite, in particular the eviction-like ones.
Although the inclination is always disturbed while crossing one eviction-like
resonance, capture can only occur when the semi-major axis is decreasing. This
is, for instance, the case of Phobos, the largest satellite of Mars, that will
cross some of these resonances in the future because its orbit is shrinking
owing to tidal effects. We estimate the impact of resonance crossing in the
orbit of the satellite, including the capture probabilities, as a function of
several parameters, such as the eccentricity and the inclination of the
satellite, and the obliquity of the planet. Finally, we use the method of the
frequency map analysis to study the resonant dynamics based on stability maps,
and we show that some of the secular resonances may overlap, which leads to
chaotic motion for the inclination of the satellite.
