A Frobenius Theorem for Corank-1 Continuous Distributions in Dimensions two and three

Abstract

We formulate a notion of (uniform) asymptotic involutivity and show that it implies (unique) integrability of corank-1 continuous distributions in dimensions three or less. This generalizes and extends a classical theorem of Frobenius Theorem which says that an involutive C^1 distribution is uniquely integrable.

29 pages. Final Version. Added more general version of result, application to ODE's, PDE's and Dynamical Systems