Manning, Anthony (2002) A Markov partition that reflects the geometry of a hyperbolic toral automorphism. American Mathematical Society. Transactions, Vol.354 (No.7). pp. 2849-2863. doi:10.1090/S0002-9947-02-03003-9 ISSN 0002-9947.

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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 (nu) 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.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science, Engineering and Medicine > Science > Mathematics
Library of Congress Subject Headings (LCSH):	Markov processes, Automorphisms, Torus (Geometry)
Journal or Publication Title:	American Mathematical Society. Transactions
Publisher:	American Mathematical Society
ISSN:	0002-9947
Official Date:	2002
Dates:	Date Event 2002 Published
Volume:	Vol.354
Number:	No.7
Page Range:	pp. 2849-2863
DOI:	10.1090/S0002-9947-02-03003-9
Status:	Peer Reviewed
Access rights to Published version:	Open Access (Creative Commons)

Data sourced from Thomson Reuters' Web of Knowledge

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