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- Title
Integrability of continuous bundles.
- Authors
Luzzatto, Stefano; Tureli, Sina; War, Khadim
- Abstract
We give new sufficient conditions for the integrability and unique integrability of continuous tangent subbundles on manifolds of arbitrary dimension, generalizing Frobenius' classical theorem for C 1 {C^{1}} subbundles. Using these conditions, we derive new criteria for uniqueness of solutions to ODEs and PDEs 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.
- Subjects
DYNAMICAL systems; MANIFOLDS (Mathematics)
- Publication
Journal für die Reine und Angewandte Mathematik, 2019, Vol 2019, Issue 752, p229
- ISSN
0075-4102
- Publication type
Article
- DOI
10.1515/crelle-2016-0049