  We associate to each non-degenerate smooth interval map a number measuring
its global asymptotic expansion. We show that this number can be calculated in
various different ways. A consequence is that several natural notions of
nonuniform hyperbolicity coincide. In this way we obtain an extension to
interval maps with an arbitrary number of critical points of the remarkable
result of Nowicki and Sands characterizing the Collet-Eckmann condition for
unicritical maps. This also solves a conjecture of Luzzatto in dimension 1.
  Combined with a result of Nowicki and Przytycki, these considerations imply
that several natural nonuniform hyperbolicity conditions are invariant under
topological conjugacy. Another consequence is for the thermodynamic formalism
of non-degenerate smooth interval maps: A non-degenerate smooth map has a
high-temperature phase transition if and only if it is not Lyapunov hyperbolic.
