Integrability vs non-integrability of distributions: Frobenius vs Chow
by Ngo, Khanh Q., M.A., SAN JOSE STATE UNIVERSITY, 2011, 67 pages; 1505737

Abstract:

In this thesis, we explore the following question: what is the accessible set of a distribution H on a smooth manifold M? In particular, when is the accessible set the entire manifold M and when does H give rise to a foliation of M? The first question is answered by a theorem of Chow, the second by a theorem of Frobenius. The intermediate case – when the accessible sets are of dimension between the dimensions of H and that of M – is answered by Sussmann's Orbit Theorem. After introducing the necessary concepts, we prove Chow's and Frobenius's Theorem (the former one in a special case) and describe some of their applications.

 
AdviserSlobodan N. Simic
SchoolSAN JOSE STATE UNIVERSITY
SourceMAI/ 50-04, p. , Feb 2012
Source TypeThesis
SubjectsMathematics
Publication Number1505737
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