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.
Demers, Mark and Wojtkowski, Marciej P., "A family of pseudo-Anosov maps" (2009). Math & Computer Science Faculty Publications. 45.
Mark Demers and Maciej P. Wojtkowski, "A family of pseudo-Anosov maps," Nonlinearity, 22:7 (2009), 1743-1760.