We provide a sufficient condition for the completeness of a time-dependent vector field in RN , generalizing the well-known left-invariance condition on Lie groups. This result can be applied to the construction of Lie groups associated to suitable families X of Hormander vector fields, without the need to use the Third Fundamental Theorem of Lie. Further applications are given to the control-theoretic distance related to X, and to the existence of the relevant geodesics.

A completeness result for time-dependent vector fields and applications

Biagi, S.;
2015-01-01

Abstract

We provide a sufficient condition for the completeness of a time-dependent vector field in RN , generalizing the well-known left-invariance condition on Lie groups. This result can be applied to the construction of Lie groups associated to suitable families X of Hormander vector fields, without the need to use the Third Fundamental Theorem of Lie. Further applications are given to the control-theoretic distance related to X, and to the existence of the relevant geodesics.
2015
Hormander vector fields; Campbell-Baker-Hausdorff-Dynkin Theorem; Third Theorem of Lie; Carnot–Carath ́eodory metric; completeness of vector fields.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11311/1125146
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