Institute for Mathematical Sciences

Preprint ims01-02

A. de Carvalho and T. Hall
The Forcing Relation for Horseshoe Braid Types.

Abstract: This paper presents evidence for a conjecture concerning the structure of the set of braid types of periodic orbits of Smale's horseshoe map, partially ordered by Boyland's forcing order. The braid types are partitioned into totally ordered subsets, which are defined by parsing the symbolic code of a periodic orbit into two segments, the {\em prefix} and the {\em decoration}: the set of braid types of orbits with each given decoration is totally ordered, the order being given by the unimodal order on symbol sequences. The conjecture is supported by computer experiment, by proofs of special cases, and by intuitive argument in terms of pruning theory.
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