During this talk I will describe the phase space structures related to the semi-major axis of
Molniya-like artifical satellites subject to tesseral and lunisolar resonances. In particular, I will
discuss the dynamics beyond the resonant integrable approximation. By using tractable models
averaged over fast angles, I will delineate the hyperbolic structures organising the long-term dy-
namics via Fast Lyapunov Indicators cartography. Finally, based on the publicly available two-line
elements space orbital data, I will provide evidence that two satellites, namely M1-69 and M1-87,
display fingerprints consistent with the dynamics associated to the hyperbolic set. This research
therefore reports on actual artificial satellites in the near-Earth environment whose dynamics are
ruled by manifolds and resonant mechanisms.

This is a joint work with Elisa Maria Alessi, Joseph O'Leary, Anne Lemaitre and Alberto Buzzoni.