On finsler entropy of smooth distributions and Stefan-Sussman foliations

2015/06/10 by F. Pelletier, Pelletier, F.
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #math.DG

paper · pdf · doi:10.48550/arxiv.1506.03205

arxiv created 2015/06/10 · arxiv updated 2015/06/11

Abstract

Using the definition of entropy of a family of increasing distances on a compact metric set given in [10] we introduce a notion of Finsler entropy for smooth distributions and Stefan-Sussmann foliations. This concept generalizes most of classical topological entropy on a compact Riemannian manifold : the entropy of a flow ([9]), of a regular foliation ([11]), of a regular distribution ([5]) and of a geometrical structure ([22]). The essential results of this paper is the nullity of the Finsler entropy for a controllable distribution and for a singular Riemannian foliation.

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