On Sussmann theorem for orbits of sets of vector fields on Banach manifolds

被引：2

作者：

Lathuille, A. ^{[1
]}

Pelletier, F. ^{[1
]}

机构：

[1] Univ Savoie, Math Lab, F-73376 Le Bourgel Lac, France

来源：

BULLETIN DES SCIENCES MATHEMATIQUES | 2012年 / 136卷 / 05期

关键词：

Banach manifold; Weak Banach submanifold; Families of vector fields; l(1)-Orbit; Weak distribution; l(1)-Distribution; Invariance; Integral manifold; Control theory; Accessibility; BILINEAR-SYSTEMS;

D O I：

10.1016/j.bulsci.2011.12.007

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The purpose of this paper is to give some generalizations, in the context of Banach manifolds, of Sussmann's results about the orbits of families of vector fields (Sussmann, 1973 [16]). Essentially, we define the notion of "l(1)-orbits" for any family of vector fields on a Banach manifold, and we prove, under appropriate assumptions, that such an orbit is a weak Banach submanifold. (c) 2011 Elsevier Masson SAS. All rights reserved.

引用

页码：579 / 616

页数：38

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