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.File in questo prodotto:
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