Dynamics and the Godbillon-Vey Class of C 1 Foliations ∗

@inproceedings{Hurder2000DynamicsAT,
  title={Dynamics and the Godbillon-Vey Class of C 1 Foliations ∗},
  author={Steven Hurder and Remi Langevin},
  year={2000}
}
We give a direct proof that a codimension–one, C-foliation F with non-zero Godbillon–Vey class GV (F) ∈ H(M) has a hyperbolic resilient leaf. Our approach is based on methods of C-dynamics, and does not use the classification theory of C-foliations. We first prove that for a codimension–one C-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-foliation F , then F… CONTINUE READING

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