A Bernoulli linked-twist map in the plane

Details A Bernoulli linked-twist map in the plane A Bernoulli linked-twist map in the plane

2008-12-13

arxiv.org/abs/0812.2552v1

Mathematics

Dynamical Systems

13 pages, 8 figures, high quality figures on request

Scientific paper

We prove that a Lebesgue measure-preserving linked-twist map defined in the plane is metrically isomorphic to a Bernoulli shift (and thus strongly mixing). This is the first such result for an explicitly defined linked-twist map on a manifold other than the two-torus. Our work builds on that of Wojtkowski who established an ergodic partition for this example using an invariant cone-field in the tangent space.

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