ODE trajectories as abnormal curves in Carnot groups

[摘要] We prove that for every polynomial ODE there exists a Carnot group where the trajectories of the ODE lift to abnormal curves. The proof defines an explicit construction to determine a covector for the resulting abnormal curves. Using this method we give new examples of abnormal curves in Carnot groups of high step. As a byproduct of the argument, we also prove that concatenations of abnormal curves have abnormal lifts. (c) 2021 Elsevier Inc. All rights reserved.

[发布日期] 2021-11-05

[关键词] Carnot groups;Sub-Riemannian geometry;Abnormal extremals