Foliating Metric Spaces: A Generalization of Frobenius' Theorem
Calcaterra, Craig
Commun. Math. Anal., Tome 11 (2011) no. 1, p. 1-40 / Harvested from Project Euclid
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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.
Publié le : 2011-01-15
Classification:  metric space,  Banach space,  flow,  nonsmooth,  infinite-dimensional control theory,  Nagumo-Brézis Theorem,  51F99,  93B29,  53C12 
@article{1293054272,
     author = {Calcaterra, Craig},
     title = {Foliating Metric Spaces: A Generalization of Frobenius' Theorem},
     journal = {Commun. Math. Anal.},
     volume = {11},
     number = {1},
     year = {2011},
     pages = { 1-40},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1293054272}
}

Calcaterra, Craig. Foliating Metric Spaces: A Generalization of Frobenius' Theorem. Commun. Math. Anal., Tome 11 (2011) no. 1, pp.  1-40. http://gdmltest.u-ga.fr/item/1293054272/