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2002 The forcing relation for horseshoe braid types
Toby Hall, André de Carvalho
Experiment. Math. 11(2): 271-288 (2002).


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 prefix and the 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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Toby Hall. André de Carvalho. "The forcing relation for horseshoe braid types." Experiment. Math. 11 (2) 271 - 288, 2002.


Published: 2002
First available in Project Euclid: 3 September 2003

zbMATH: 1116.37307
MathSciNet: MR1959268

Primary: 37Exx
Secondary: 37Cxx , 57M25

Keywords: braid forcing , Horseshoe periodic orbits

Rights: Copyright © 2002 A K Peters, Ltd.


Vol.11 • No. 2 • 2002
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