We extend Weitzman's (1998) recombinant growth framework to include endogenous R&D decisions. The analysis is carried out in the (knowledge-capital) state space by means of two characteristic curves: one is identified as a turnpike along which growing economies evolve; the other attracts stagnating economies. Sustained growth depends on a condition relating the slopes of the characteristic curves as well as on a minimal endowment requirement. A growing economy reaches the turnpike at a most rapid R&D rate and evolves along it thereafter. In the long run, the rate of growth and the income shares devoted to R&D, saving and consumption approach constant values that depend on the asymptotic characteristic slopes.