A family of pseudo-Anosov maps
نویسندگان
چکیده
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.
منابع مشابه
On Representations of Certain Pseudo-anosov Maps of Riemann Surfaces with Punctures
Let S be a Riemann surface of type (p, n) with 3p + n > 4 and n ≥ 1. Let α1, α2 ⊂ S be two simple closed geodesics such that {α1, α2} fills S. It was shown by Thurston that most maps obtained through Dehn twists along α1 and α2 are pseudo-Anosov. Let a be a puncture. In this paper, we study the family F(S, a) of pseudo-Anosov maps on S that projects to the trivial map as a is filled in, and sho...
متن کاملar X iv : 0 81 2 . 29 41 v 1 [ m at h . G T ] 1 5 D ec 2 00 8 ENTROPY VS VOLUME FOR PSEUDO - ANOSOV MAPS
We will discuss theoretical and experimental results concerning comparison of entropy of pseudo-Anosov maps and volume of their mapping tori. Recent study of Weil-Petersson geometry of the Teichmüller space tells us that they admit linear inequalities for both sides under some bounded geometry condition. We construct a family of pseudo-Anosov maps which violates one side of inequalities under u...
متن کاملNew Infinite Families of Pseudo-anosov Maps with Vanishing Sah-arnoux-fathi Invariant
We show that an orientable pseudo-Anosov homeomorphism has vanishing SahArnoux-Fathi invariant if and only if the minimal polynomial of its dilatation is not reciprocal. We relate this to works of Margalit-Spallone and Birman, Brinkmann and Kawamuro. Mainly, we use Veech’s construction of pseudo-Anosov maps to give explicit pseudo-Anosov maps of vanishing Sah-Arnoux-Fathi invariant. In particul...
متن کاملExtensions, 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.
متن کاملAn asymptotic behavior of the dilatation for a family of pseudo-Anosov braids
The dilatation of a pseudo-Anosov braid is a conjugacy invariant. In this paper, we study the dilatation of a special family of pseudo-Anosov braids. We prove an inductive formula to compute their dilatation, a monotonicity and an asymptotic behavior of the dilatation for this family of braids. We also give an example of a family of pseudo-Anosov braids with arbitrarily small dilatation such th...
متن کامل