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.

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.
Annamaria Montanari; Daniele Morbidelli
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/172659
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