  We describe the phase space structures related to the semi-major axis of
Molniya-like satellites subject to tesseral and lunisolar resonances. In
particular, the questions answered in this contribution are: (i) we study the
indirect interplay of the critical inclination resonance on the
semi-geosynchronous resonance using a hierarchy of more realistic dynamical
systems, thus discussing the dynamics beyond the integrable approximation. By
introducing ad hoc tractable models averaged over fast angles, (ii) we
numerically demarcate the hyperbolic structures organising the long-term
dynamics via Fast Lyapunov Indicators cartography. Based on the publicly
available two-line elements space orbital data, (iii) we identify two
satellites, namely Molniya 1-69 and Molniya 1-87, displaying fingerprints
consistent with the dynamics associated to the hyperbolic set. Finally, (iv)
the computations of their associated dynamical maps highlight that the
spacecraft are trapped within the hyperbolic tangle. This research therefore
reports evidence of actual artificial satellites in the near-Earth environment
whose dynamics are ruled by manifolds and resonant mechanisms. The tools,
formalism and methodologies we present are exportable to other region of space
subject to similar commensurabilities as the geosynchronous region.
