Bernoulli linked-twist maps in the plane

摘要

We prove that certain area-preserving linked-twist maps defined in the plane are metrically isomorphic to a Bernoulli shift. This is the first such result for explicitly defined linked-twist maps on a manifold other than the two-torus. Our work builds on that of Wojtkowski [Linked twist mappings have the K-property, Nonlinear dynamics; Proceedings of the International Conference, New York, NY, December 17-21, 1979] who established an ergodic partition for the maps in question, using an invariant cone field in the tangent space.