On the name.
The science behind it
In 1963, Edward Lorenz showed that in nonlinear dynamical systems, arbitrarily small differences in initial conditions grow exponentially into system-scale divergences. Nine years later he gave the phenomenon its permanent name, in the title of a talk: “Does the flap of a butterfly's wings in Brazil set off a tornado in Texas?”
The gravitational N-body problem is exactly such a system. Near planetary close encounters, neighboring trajectories diverge exponentially — which is why the long-term prediction of certain asteroid orbits is hard, and why the steering of those same orbits is, counterintuitively, cheap. A millimeter-per-second impulse applied years before a gravitational-keyhole passage is amplified by planetary gravity into kilometer-per-second-scale changes in the orbit that follows. Chaos, the forecaster's adversary, is UB's amplifier of action.
This mechanism answers a question larger than habitat construction: by what path does a civilization whose power is measured in gigawatts obtain outcomes measured in planets? On Kardashev's 1964 scale, commanding planetary masses and energies is the mark of a Type I civilization — a status centuries away by any extrapolation of raw energy growth. Sensitive dependence collapses that gap for a specific and precious class of problems: wherever a system is chaotic and foresight is long, small forces applied at the sensitive point purchase planetary-scale results. Orbital mechanics is the largest such system within human reach.
The butterfly is therefore both the Program's method — decades of foresight, grams of force, planets of consequence — and its thesis about how a young species grows:
References: Lorenz (1963), Journal of the Atmospheric Sciences; Lorenz (1972), AAAS; Kardashev (1964), Soviet Astronomy. Full treatment in white paper §1.3 and §2.3 — read it here.