Dynamical properties of quasihyperbolic toral automorphisms

@article{Lind1982DynamicalPO,
  title={Dynamical properties of quasihyperbolic toral automorphisms},
  author={Douglas Lind},
  journal={Ergodic Theory and Dynamical Systems},
  year={1982},
  volume={2},
  pages={49 - 68}
}
  • D. Lind
  • Published 1 March 1982
  • Mathematics
  • Ergodic Theory and Dynamical Systems
Abstract 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… 
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