Almost exponential maps and integrability results for a class of horizontally regular vector fields

Abstract

We show a higher order integrability theorem for distributions generated by a family of vector fields under a horizontal regularity assumption on their coefficients. We use as chart a class of almost exponential maps which we discuss in details

arXiv admin note: material from arXiv:1106.2410v1, now three separate articles arXiv:1106.2410v2, arXiv:1201.5228, arXiv:1201.5209

References in corpus (3)

• A Frobenius-type theorem for singular Lipschitz distributions
• Generalized Jacobi identities and ball-box theorem for horizontally regular vector fields
• Integrability of weak distributions on Banach manifolds

Cited by in corpus (5)

• A Frobenius-type theorem for singular Lipschitz distributions
• Generalized Jacobi identities and ball-box theorem for horizontally regular vector fields
• Step-s involutive families of vector fields, their orbits and the Poincaré inequality
• Integral representation for bracket-generating multi-flows
• A Hadamard-type open map theorem for submersions and applications to completeness results in Control Theory