La décomposition dynamique et la différentiabilité des feuilletages des surfaces
Annales de l'Institut Fourier, Volume 37 (1987) no. 3, p. 85-116

Let be a singular foliation on a compact surface M. In order to analyse the dynamics of , one can canonically cut up M into subsurfaces bounded by curves transverse to : the components of the recurrence of (quasiminial sets) are contained in the “regions of recurrence” and may be studied separately; on the other hand, the dynamics is trivial in the other regions (“regions of passage”). The paper also offers a definition of a singular foliation of classe C r on M, and studies the topological and dynamical features of C 2 (or C ) on M, and studies the topological and dynamical features of C 2 (or C ) foliations.

Soit un feuilletage singulier d’une surface compacte M. Pour analyser la dynamique de , on décompose M de façon canonique en sous-surfaces bordées par des courbes transverses à  : les composantes de la récurrence de (ensembles quasiminimaux) sont contenues dans les “régions de récurrence” et peuvent être étudiées séparément; par contre dans les autres régions, dites “régions de passage”, la dynamique est triviale. On propose ensuite une définition des feuilletages singuliers de classe C r sur les surfaces, et on étudie quelles restrictions l’hypothèse que est C 2 (ou C ) impose à la topologie et à la dynamique du feuilletage.

@article{AIF_1987__37_3_85_0,
     author = {Levitt, Gilbert},
     title = {La d\'ecomposition dynamique et la diff\'erentiabilit\'e des feuilletages des surfaces},
     journal = {Annales de l'Institut Fourier},
     publisher = {Institut Fourier},
     address = {Grenoble},
     volume = {37},
     number = {3},
     year = {1987},
     pages = {85-116},
     doi = {10.5802/aif.1099},
     zbl = {0596.57019},
     mrnumber = {88m:57035},
     language = {fr},
     url = {http://www.numdam.org/item/AIF_1987__37_3_85_0}
}
Levitt, Gilbert. La décomposition dynamique et la différentiabilité des feuilletages des surfaces. Annales de l'Institut Fourier, Volume 37 (1987) no. 3, pp. 85-116. doi : 10.5802/aif.1099. http://www.numdam.org/item/AIF_1987__37_3_85_0/

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