Integrability of Continuous Bundles
Classical Analysis and ODEs
2016-10-11 v2 Dynamical Systems
Abstract
We give new sufficient conditions for the integrability and unique integrability of continuous tangent sub-bundles on manifolds of arbitrary dimension, generalizing Frobenius' classical Theorem for C^1 sub-bundles. Using these conditions we derive new criteria for uniqueness of solutions to ODE's and PDE's and for the integrability of invariant bundles in dynamical systems. In particular we give a novel proof of the Stable Manifold Theorem and prove some integrability results for dynamically defined dominated splittings.
Keywords
Cite
@article{arxiv.1606.00343,
title = {Integrability of Continuous Bundles},
author = {Stefano Luzzatto and Sina Tureli and Khadim War},
journal= {arXiv preprint arXiv:1606.00343},
year = {2016}
}
Comments
40 pages, 5 figures. To appear in Crelle's Journal