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

Eiko Kin

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arXiv · 0711.4398

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

Eiko Kin

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Abstract

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.

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Eiko Kin. 2007-11-28. The forcing partial order on a family of braids forced by pseudo-Anosov 3-braids. https://arxiv.org/abs/0711.4398

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