scholarly journals Nonsmooth Hörmander vector fields and their control balls

2012 ◽  
Vol 364 (5) ◽  
pp. 2339-2375 ◽  
Author(s):  
Annamaria Montanari ◽  
Daniele Morbidelli
Keyword(s):  
Vector Fields ◽  
Hörmander Vector Fields

A completeness result for time-dependent vector fields and applications

2015 ◽  
Vol 17 (04) ◽  
pp. 1450040 ◽  
Author(s):  
Stefano Biagi ◽  
Andrea Bonfiglioli
Keyword(s):  
Vector Field ◽  
Lie Groups ◽  
Vector Fields ◽  
Time Dependent ◽  
Sufficient Condition ◽  
Invariance Condition ◽  
The Third ◽  
Completeness Result ◽  
Dependent Vector ◽  
Hörmander Vector Fields

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 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.

Sign in / Sign up

Export Citation Format

Share Document