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2011 Foliating Metric Spaces: A Generalization of Frobenius' Theorem
Craig Calcaterra
Commun. Math. Anal. 11(1): 1-40 (2011).


Using families of curves to generalize vector fields, the Lie bracket is defined on a metric space, $M$. For $M$ complete, versions of the local and global Frobenius theorems hold, and flows are shown to commute if and only if their bracket is zero. An example is given showing $L^{2}\left( \mathbb{R}\right) $ is controllable by two elementary flows.


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Craig Calcaterra. "Foliating Metric Spaces: A Generalization of Frobenius' Theorem." Commun. Math. Anal. 11 (1) 1 - 40, 2011.


Published: 2011
First available in Project Euclid: 22 December 2010

zbMATH: 1215.37020
MathSciNet: MR2753677

Primary: 51F99
Secondary: 53C12 , 93B29

Keywords: Banach space , flow , infinite-dimensional control theory , metric space , Nagumo-Brézis Theorem , nonsmooth

Rights: Copyright © 2011 Mathematical Research Publishers

Vol.11 • No. 1 • 2011
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