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

2014/11/21 by Stefano Luzzatto, Luzzatto, Stefano, Sina Türeli +3
Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #Dynamical Systems (math.DS) #FOS: Mathematics #Functional Equations Stability Results #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.1411.5896

openalex publication_date 2014/11/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We formulate a notion of (uniform) asymptotic involutivity and show that it\nimplies (unique) integrability of corank-1 continuous distributions in\ndimensions three or less. This generalizes and extends a classical theorem of\nFrobenius Theorem which says that an involutive C¹ distribution is uniquely\nintegrable.\n

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