Regularity and Continuity Properties of the Sub-Riemannian Exponential Map-Reference-Cited by-同舟云学术

Regularity and Continuity Properties of the Sub-Riemannian Exponential Map

Published:2023-01-26 Issue:4 Volume:29 Page:1385-1407
ISSN:1079-2724
Container-title:Journal of Dynamical and Control Systems
language:en
Short-container-title:J Dyn Control Syst

Author:

Borza Samuël^ORCID,Klingenberg Wilhelm

Abstract

AbstractWe prove a version of Warner’s regularity and continuity properties for the sub-Riemannian exponential map. The regularity property is established by considering sub-Riemannian Jacobi fields while the continuity property follows from studying the Maslov index of Jacobi curves. We finally show how this implies that the exponential map of the three-dimensional Heisenberg group is not injective in any neighbourhood of a conjugate vector.

Funder

Engineering and Physical Sciences Research Council

HORIZON EUROPE European Research Council

Publisher

Springer Science and Business Media LLC

Subject

Control and Optimization,Numerical Analysis,Algebra and Number Theory,Control and Systems Engineering

Link

https://link.springer.com/content/pdf/10.1007/s10883-022-09624-y.pdf

Reference13 articles.

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