Topological Entropy of Pseudo-Anosov Maps from a Typical Thurston’s Construction

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...

Heegaard Splittings and Pseudo-anosov Maps

LetM andM− be oriented 3-dimensional handlebodies whose boundary is identified with an oriented surface S of genus g > 1 in such a way that the orientation of S agrees with the orientation of ∂M and does not with the one of ∂M−. Given a mapping class f ∈ MCG(S) we consider the closed, oriented 3-manifold Nf =M + ∪f M− obtained by identifying the boundaries of M and M− via f . In this note we st...

Extensions, Quotients and Generalized Pseudo-anosov Maps

We describe a circle of ideas relating the dynamics of 2-dimensional homeomorphisms to that of 1-dimensional endomorphisms. This is used to introduce a new class of maps generalizing that of Thurston’s pseudo-Anosov homeomorphisms.

A Note on Pseudo-Anosov Maps with Small Growth Rate

We present an explicit sequence of pseudo-Anosov maps φk : S2k → S2k of surfaces of genus 2k whose growth rates converge to one. Introduction In this note, we present an explicit sequence φk of pseudo-Anosov of surfaces of genus 2k whose growth rates converge to one. This answers a question of Joan Birman, who had previously asked whether such growth rates are bounded away from one. Norbert A’C...

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