A family of pseudo-Anosov maps

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Published 11 June 2009 • 2009 IOP Publishing Ltd and London Mathematical Society
, , Citation Mark F Demers and Maciej P Wojtkowski 2009 Nonlinearity 22 1743 DOI 10.1088/0951-7715/22/7/013

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Author affiliations

1 Department of Mathematics and Computer Science, Fairfield University, Fairfield CT, 06824 USA

2 Department of Mathematics and Informatics, University of Warmia and Mazury, ul Zolnierska 14, 10-561 Olsztyn, Poland

Dates

  1. Received 23 April 2009
  2. Published

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0951-7715/22/7/1743

Abstract

We study a family of area-preserving maps of the 2-torus and show that they are pseudo-Anosov. We present a method to construct finite Markov partitions for this family which utilizes their common symmetries. Through these partitions we show explicitly that each map is a tower over a first return map, intimately linked to a toral automorphism. This enables us to calculate directly some dimensional characteristics of the dynamics.

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