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We discuss a comparison of the entropy of pseudo-Anosov maps and the volume of their mapping tori. Recent study of Weil-Petersson geometry of the Teichmüller space tells us that they admit linear inequalities for both directions under some bounded geometry condition. Based on the experiments, we present various observations on the relation between minimal… (More)

- Eriko Hironaka, Eiko Kin
- 2005

This paper describes a family of pseudo–Anosov braids with small dilatation. The smallest dilatations occurring for braids with 3, 4 and 5 strands appear in this family. A pseudo-Anosov braid with 2g + 1 strands determines a hyperelliptic mapping class with the same dilatation on a genus–g surface. Penner showed that logarithms of least dilatations of… (More)

We consider a hyperbolic surface bundle over the circle with the smallest known volume among hyperbolic manifolds having 3 cusps, so called " the magic manifold " M = M magic. We compute the entropy function on the fiber face ∆ ⊂ H 2 (M, ∂M ; R), determine homology classes whose representatives are genus 0 fiber surfaces, and describe their monodromies by… (More)

- pseudo–Anosov 3–braids, Eiko Kin
- 2008

Li–York theorem tells us that a period 3 orbit for a continuous map of the interval into itself implies the existence of a periodic orbit of every period. This paper concerns an analogue of the theorem for homeomorphisms of the 2–dimensional disk. In this case a periodic orbit is specified by a braid type and on the set of all braid types Boyland's… (More)

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… (More)

- Robert Ghrist, Eiko Kin
- 2004

Let K be a knot or link in S 3 which is fibred — the complement fibres over S 1 with fibres spanning surfaces. We focus on those fibred knots and links which have the following property: every vector field transverse to the fibres possesses closed flow lines of all possible knot and link types in S 3. Our main result is that a large class of fibred knots… (More)

We study the magic manifold N which is a hyperbolic and fibered 3-manifold. We give an explicit construction of a fiber Fa and its monodromy : Fa → Fa of the fibration associated to each fibered class a of N. Let δg (resp. δ + g) be the minimal dilatation of pseudo-Anosovs (resp. pseudo-Anosovs with orientable invariant foliations) defined on an orientable… (More)

- Robert Ghrist, Eiko Kin
- 2003

Let K be a knot or link in S 3 which is fibred — the complement fibres over S 1 with fibres spanning surfaces. We focus on those fibred knots and links which have the following property: every vector field transverse to the fibres possesses closed flow lines of all possible knot and link types in S 3. Our main result is that a large class of fibred knots… (More)

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