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Whereas subriemannian geometry usually deals with smooth horizontaldistributions, partially hyperbolic dynamical systems provide many examples ofsubriemannian geometries defined by non-smooth (namely, H\"older continuous)distributions. These distributions are of great significance for the behaviorof the parent dynamical system. The study of H\"older subriemannian geometriescould therefore offer new insights into both dynamics and subriemanniangeometry. In this paper we make a small step in that direction: we prove aH\"older-type lower bound on the subriemannian distance for H\"older continuousnowhere integrable codimension one distributions. This bound generalizes thewell-known square root bound valid in the smooth case.

A lower bound on the subriemannian distance for H\"older distributions