Transversals to laminations

Russell Bruce Walker

Vol. 99 (1982), No. 2, 483–490

DOI: 10.2140/pjm.1982.99.483

Abstract

The stable and unstable manifolds of an Anosov diffeomorphism are not leaves of C¹-foliation. Instead, their unions comprise two laminations; that is, two C⁰-foliations which have C¹-smooth leaves and continuous nonsingular tangent plane fields. Recently C. Ennis has shown that laminations have transversals at every point. In this note, the existence of transversals is shown to require plane field continuity.

Mathematical Subject Classification 2000

Primary: 57R30

Milestones

Received: 4 June 1979

Published: 1 April 1982