A dynamical approach to the Sard problem in Carnot groups

TL;DR

This paper presents a dynamical-systems method to address the Sard problem in Carnot groups, showing that singular curves can be constructed from specific dynamical trajectories and providing positive solutions in certain classes.

Contribution

It introduces a novel dynamical approach to the Sard problem in Carnot groups, enabling the construction of singular curves from dynamical system trajectories.

Findings

Singular curves can be generated by concatenating dynamical system trajectories.

The approach yields positive solutions to the Sard problem in some Carnot group classes.

The method offers a new perspective for analyzing sub-Riemannian geometry problems.

Abstract

We introduce a dynamical-systems approach for the study of the Sard problem in sub-Riemannian Carnot groups. We show that singular curves can be obtained by concatenating trajectories of suitable dynamical systems. As an applications, we positively answer the Sard problem in some classes of Carnot groups.