XXXVIII Workshop on Geometric Methods in Physics | 30.06-6.07.2019 |

VIII School on Geometry and Physics | 24-28.06.2019 |

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## Fernand Pelletier## On the Finslerian entropy of smooth distributions and Stefan-Sussman foliationsStarting from the definition of the entropy of a growing family of distances on a compact metric space, we define the Finslerian entropy of a smooth distribution and of a Stefan-Sussman foliation. This notion of entropy is a generalization of most classical topological entropies on a Riemannian compact manifold: the entropy of a flow ([2]), of a regular foliation ([4]), of a regular distribution ([1]) and more generally of a ”geometrical structure” ([5]). In this way, we obtain the nullity of the Finslerian entropy of a controllable distribution and of a singular Riemannian foliation. References [1] A. Biś: Entropy of distributions Topology Appl. 152, No. 1-2 , pp2-10,(2005). [2] E. I. Dinaburg: On the relations among various entropy characteristics of dynamical systems, Izv. Akad. Nauk SSSR 35 (1971). [3] T-C. Dinh, V-A. Nguyen and N. Sibony: Entropy for hyperbolic Riemann surface laminations I arXiv:1105.2307. [4] E. Ghys, R. Langevin and P. Walczak: Entropie géométrique des feuilletages Acta Math., 160, no. 1-2, 105-142, (1988). [5] N-T. Zung: Entropy of geometric structures Bulletin Brazilian Mathematical Society New series, Vol 42, 4, pp 853-867, (2011) |

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