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de Carvalho, André; Hall, Toby

The forcing relation for horseshoe braid types. (English) Zbl 1116.37307

Exp. Math. 11, No. 2, 271-288 (2002).
Summary: 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.

Cited in 1 Review
Cited in 5 Documents

MSC:

37E30 Dynamical systems involving homeomorphisms and diffeomorphisms of planes and surfaces
37B10 Symbolic dynamics
37B40 Topological entropy
57M25 Knots and links in the \(3\)-sphere (MSC2010)

Keywords:

Horseshoe periodic orbits; braid forcing

Software:

Horseshoe
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Full Text: DOI Euclid EuDML

References:

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