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Induced maps of Bernoulli dynamical systems

By Matthew Nicol


<p>Let (<i>f, T<sup>n</sup>, mu</i>) be a linear hyperbolic automorphism of the <i>n</i>-torus. We show that if <i>A</i> ⊂ <i>T<sup>n</sup></i> has a boundary which is a finite union of <i>C</i><sup>1</sup> submanifolds which have no tangents in the stable (<i>E<sup>s</sup></i>) or unstable (<i>E<sup>u</sup></i>) direction then the induced map on <i>A</i>, (<i>f<sub>A</sub>,A, mu<sub>A</sub></i>) is also Bernoulli. We show that Poincáre maps for uniformly transverse <i>C</i><sup>1</sup> Poincáre sections in smooth Bernoulli Anosov flows preserving a volume measure are Bernoulli if they are also transverse to the strongly stable and strongly unstable foliation.</p

Year: 2001
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