We provide a sufficient condition for the completeness of a time-dependent vector field in R^N, 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 Hörmander 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.
S. Biagi, A. Bonfiglioli (2015). A completeness result for time-dependent vector fields and applications. COMMUNICATIONS IN CONTEMPORARY MATHEMATICS, 17(4), 1-26 [10.1142/S0219199714500400].
A completeness result for time-dependent vector fields and applications
BIAGI, STEFANO;BONFIGLIOLI, ANDREA
2015
Abstract
We provide a sufficient condition for the completeness of a time-dependent vector field in R^N, 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 Hörmander 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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
