A Markov Partition That Reflects the Geometry of a Hyperbolic Toral Automorphism

@inproceedings{Manning2002AMP,
  title={A Markov Partition That Reflects the Geometry of a Hyperbolic Toral Automorphism},
  author={Anthony J Manning},
  year={2002}
}
We show how to construct a Markov partition that reflects the geometrical action of a hyperbolic automorphism of the n-torus. The transition matrix is the transpose of the matrix induced by the automorphism in udimensional homology, provided this is non-negative. (Here u denotes the expanding dimension.) That condition is satisfied, at least for some power of the original automorphism, under a certain non-degeneracy condition on the Galois group of the characteristic polynomial. The (u… CONTINUE READING

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