GENERATING POSITIVE GEOMETRIC ENTROPY FROM RECURRENT LEAVES

In this paper we introduce a C-r-perturbation procedure, with respect to the C-r-Epstein topology, for CCr-foliations by surfaces. Using this perturbation procedure we show how one can use the existence of recurrent leaves of a certain C-r-foliation F to obtain a foliation G, Cr-close to F in the C-r-Epstein topology, which has a resilient leaf. In particular, one can take advantage of the recurrence property to construct examples of C-r-foliations, C-r-close to each other and such that one of them has a resilient leaf while the other is Riemannian (therefore has trivial dynamics). (AU)