A family of pseudo-Anosov maps

Citation data:

Nonlinearity, ISSN: 0951-7715, Vol: 22, Issue: 7, Page: 1743-1760

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https://digitalcommons.fairfield.edu/mathandcomputerscience-facultypubs/45; https://works.bepress.com/mark_demers/12
Mark F. Demers; MacIej P. Wojtkowski
IOP Publishing
Physics and Astronomy; Mathematics; Mathematical physics; Computational physics; Computer Sciences; Physical Sciences and Mathematics
article description
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. © 2009 IOP Publishing Ltd and London Mathematical Society.