Osaka Journal of Mathematics

The forcing partial order on a family of braids forced by pseudo-Anosov 3-braids

Eiko Kin

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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 dynamical partial order can be defined. We describe the partial order on a family of braids and show that a period 3 orbit of pseudo-Anosov braid type implies the Smale-horseshoe map which is a factor possessing complicated chaotic dynamics.

Article information

Osaka J. Math., Volume 45, Number 3 (2008), 757-772.

First available in Project Euclid: 17 September 2008

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 37E30: Homeomorphisms and diffeomorphisms of planes and surfaces 57M27: Invariants of knots and 3-manifolds
Secondary: 57M50: Geometric structures on low-dimensional manifolds


Kin, Eiko. The forcing partial order on a family of braids forced by pseudo-Anosov 3-braids. Osaka J. Math. 45 (2008), no. 3, 757--772.

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