  We analyze energy spreading for a system that features mixed chaotic
phase-space, whose control parameters (or slow degrees of freedom) vary
quasi-statically. For demonstration purpose we consider the restricted 3~body
problem, where the distance between the two central stars is modulated due to
their Kepler motion. If the system featured hard-chaos, one would expect
diffusive spreading with coefficient that can be estimated using
linear-response (Kubo) theory. But for mixed phase space the chaotic sea is
multi-layered. Consequently, it becomes a challenge to find a robust procedure
that translates the sticky dynamics into a stochastic model. We propose a
Poincar\'e-sequencing method that reduces the multi-dimensional motion into a
one-dimensional random-walk in impact-space. We test the implied relation
between stickiness and the rate of spreading.
