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

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- by Anthony Manning PDF
- Trans. Amer. Math. Soc.
**354**(2002), 2849-2863 Request permission

## Abstract:

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 $u$-dimensional 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 $(^n_u)$ rectangles are constructed by an iterated function system, and they resemble the product of the projection of a $u$-dimensional face of the unit cube onto the unstable subspace and the projection of minus the orthogonal $(n-u)$-dimensional face onto the stable subspace.## References

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## Additional Information

**Anthony Manning**- Affiliation: Mathematics Institute, University of Warwick, Coventry, CV4 7AL, UK
- Email: akm@maths.warwick.ac.uk
- Received by editor(s): September 4, 2001
- Published electronically: February 26, 2002
- © Copyright 2002 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**354**(2002), 2849-2863 - MSC (2000): Primary 37D20, 37B10; Secondary 28A80, 37B40
- DOI: https://doi.org/10.1090/S0002-9947-02-03003-9
- MathSciNet review: 1895206