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Dynamical properties of quasihyperbolic toral automorphisms

Published online by Cambridge University Press:  13 August 2009

D. A. Lind
D. A. Lind
Affiliation:
Department of Mathematics, University of Washington, Seattle, Washington 98195
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Abstract

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We study the dynamical properties of ergodic toral autmorphisms that have some eigenvalues of modulus one. For such automorphisms, all sufficiently fine smooth partitions generate measurably, but never topologically, and are never weak Bernoulli. The points of period k become uniformly distributed exponentially fast, and Lipschitz functions mix exponentially fast. Every reasonably smooth compact null set has the property that there is a dense set of periodic points whose entire orbit misses the set, but this is false for general compact null sets. Katznelson's property of almost weak Bernoulli can be strengthened to a certain exponential rate of independence, but breaks down at a critical number. Finally, open sets have return times that decay exponentially fast.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 2 , Issue 1 , March 1982 , pp. 49 - 68
Copyright
Copyright © Cambridge University Press 1982

References

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