Let F be a codimension-one, C^2-foliation on a manifold M without boundary.
In this work we show that if the Godbillon--Vey class GV(F) \in H^3(M) is
non-zero, then F has a hyperbolic resilient leaf. Our approach is based on
methods of C^1-dynamical systems, and does not use the classification theory of
C^2-foliations. We first prove that for a codimension--one C^1-foliation with
non-trivial Godbillon measure, the set of infinitesimally expanding points E(F)
has positive Lebesgue measure. We then prove that if E(F) has positive measure
for a C^1-foliation F, then F must have a hyperbolic resilient leaf, and hence
its geometric entropy must be positive. The proof of this uses a pseudogroup
version of the Pliss Lemma. The theorem then follows, as a C^2-foliation with
non-zero Godbillon-Vey class has non-trivial Godbillon measure. These results
apply for both the case when M is compact, and when M is an open manifold.Comment: This manuscript is a revision of the section 3 material from the
previous version, and includes edits to the pictures in the tex
