We consider a family of C (1) vector fields in a"e (n) and we discuss the associated -orbits. Namely, we assume that our vector fields belong to a horizontal regularity class and we require that a suitable s-involutivity assumption holds. Then we show that any -orbit is a C (1) immersed submanifold and it is an integral submanifold of the distribution generated by the family of all commutators up to length s. Our main tool is a class of almost exponential maps of which we discuss carefully some precise first order expansions.
Annamaria Montanari, Daniele Morbidelli (2013). Almost Exponential Maps and Integrability Results for a Class of Horizontally Regular Vector Fields. POTENTIAL ANALYSIS, 38(2), 611-633 [10.1007/s11118-012-9289-6].
Almost Exponential Maps and Integrability Results for a Class of Horizontally Regular Vector Fields
MONTANARI, ANNAMARIA;MORBIDELLI, DANIELE
2013
Abstract
We consider a family of C (1) vector fields in a"e (n) and we discuss the associated -orbits. Namely, we assume that our vector fields belong to a horizontal regularity class and we require that a suitable s-involutivity assumption holds. Then we show that any -orbit is a C (1) immersed submanifold and it is an integral submanifold of the distribution generated by the family of all commutators up to length s. Our main tool is a class of almost exponential maps of which we discuss carefully some precise first order expansions.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
