The Ball-Box Theorem for a Class of Non-differentiable Tangent Subbundles

TL;DR

This paper extends the Ball-Box Theorem to certain non-differentiable tangent subbundles in sub-Riemannian geometry, providing new insights into their geometric structure and applications to dynamical systems.

Contribution

It introduces a generalized version of the Ball-Box Theorem applicable to specific non-differentiable subbundles satisfying a geometric condition.

Findings

The theorem holds for a class of non-differentiable tangent subbundles.

Examples of such bundles are provided.

Applications to dynamical systems are demonstrated.

Abstract

We show that an analogue of the Ball-Box Theorem for step 2, completely non-integrable bundles from smooth sub-Riemannian geometry hold true for a class of non-differentiable tangent subbundles that satisfy a geometric condition. In the final section of the paper we give examples of such bundles and an application to dynamical systems.