A geometric criterion to be pseudo-Anosov

A family of pseudo-Anosov maps

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 dimensio...

On Axiom a Diffeomorphisms C0-close to Pseudo-anosov Maps

Commutative pseudo BE-algebras

The aim of this paper is to introduce the notion of commutative pseudo BE-algebras and investigate their properties.We generalize some results proved by A. Walendziak for the case of commutative BE-algebras.We prove that the class of commutative pseudo BE-algebras is equivalent to the class of commutative pseudo BCK-algebras. Based on this result, all results holding for commutative pseudo BCK-...

On Period Minimal Pseudo-anosov Braids

A family of period minimal pseudo-Anosov braids, one for each pair of Farey neighbors in (0, 1/2], is described.

Pseudo-Anosov dilatations and the Johnson filtration

Answering a question of Farb–Leininger–Margalit, we give explicit lower bounds for the dilatations of pseudo-Anosov mapping classes lying in the kth term of the Johnson filtration of the mapping class group.