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A Markov partition that reflects the geometry of a hyperbolic toral automorphism
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Manning, Anthony. (2002) A Markov partition that reflects the geometry of a hyperbolic toral automorphism. American Mathematical Society. Transactions, Vol.354 (No.7). pp. 28492863. ISSN 00029947
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Official URL: http://dx.doi.org/10.1090/S0002994702030039
Abstract
We show how to construct a Markov partition that reflects the
geometrical action of a hyperbolic automorphism of the ntorus. The transition
matrix is the transpose of the matrix induced by the automorphism in udimensional
homology, provided this is nonnegative. (Here u denotes the
expanding dimension.) That condition is satisfied, at least for some power
of the original automorphism, under a certain nondegeneracy 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 udimensional 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 > 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:  00029947  
Official Date:  2002  
Dates: 


Volume:  Vol.354  
Number:  No.7  
Page Range:  pp. 28492863  
Identifier:  10.1090/S0002994702030039  
Status:  Peer Reviewed  
Access rights to Published version:  Open Access  
References:  [1] R Adler and B Weiss, Similarity of automorphisms of the torus, Memoirs Amer. Math. Soc., 

URI:  http://wrap.warwick.ac.uk/id/eprint/4295 
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