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Conjugacies between horseshoe braids

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Published 9 May 2003 • Published under licence by IOP Publishing Ltd
, , Citation André de Carvalho and Toby Hall 2003 Nonlinearity 16 1329 DOI 10.1088/0951-7715/16/4/308

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Author affiliations

1 Institute for Mathematical Sciences, State University of New York at Stony Brook, NY 11794-3660, USA

2 Department of Mathematical Sciences, University of Liverpool, Liverpool L69 7ZL, UK

3 Current address: Instituto de Matemática e Estatística, Universidade de São Paulo, Rua do Matão, 1010, 05508-090 São Paulo, SP Brazil.

Dates

  1. Received 9 September 2002
  2. Published

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Abstract

A proof is given of part of a conjecture about the way in which the set of horseshoe braid types is organized by the forcing partial order. Horseshoe periodic orbits are labelled by their height (a rational number) and decoration (a word in the symbols 0 and 1), and it is shown that, with the exception of the so-called limit cases, periodic orbits of the same height and decoration have the same braid type.

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10.1088/0951-7715/16/4/308