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A Markov partition that reflects the geometry of a hyperbolic toral automorphism

By Anthony Manning

Abstract

We show how to construct a Markov partition that reflects the\ud geometrical action of a hyperbolic automorphism of the n-torus. The transition\ud matrix is the transpose of the matrix induced by the automorphism in u-dimensional\ud homology, provided this is non-negative. (Here u denotes the\ud expanding dimension.) That condition is satisfied, at least for some power\ud of the original automorphism, under a certain non-degeneracy condition on\ud the Galois group of the characteristic polynomial. The (nu) rectangles are\ud constructed by an iterated function system, and they resemble the product\ud of the projection of a u-dimensional face of the unit cube onto the unstable\ud subspace and the projection of minus the orthogonal (n - u)-dimensional face\ud onto the stable subspace

Topics: QA
Publisher: American Mathematical Society
Year: 2002
OAI identifier: oai:wrap.warwick.ac.uk:4295

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