Bernoulli linked-twist maps in the plane. (English) Zbl 1205.37013
Summary: 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 M. Wojtkowski [in: Nonlinear dynamics, int. Conf., New York 1979, Ann. N.Y. Acad. Sci. 357, 1288, 65–76 (1980; Zbl 0475.58008)] who established an ergodic partition for the maps in question using an invariant cone field in the tangent space.
MSC:
| 37A25 | Ergodicity, mixing, rates of mixing |
| 37D25 | Nonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory, etc.) |
| 37D50 | Hyperbolic systems with singularities (billiards, etc.) (MSC2010) |
| 37N10 | Dynamical systems in fluid mechanics, oceanography and meteorology |
| 37N99 | Applications of dynamical systems |
Citations:
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