Decoration invariants for horseshoe braids

André de Carvalho; Toby Hall

doi:10.3934/dcds.2010.27.863

Article Contents

2010, Volume 27, Issue 3: 863-906. Doi: 10.3934/dcds.2010.27.863

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Decoration invariants for horseshoe braids

André de Carvalho^1, and
Toby Hall^2,

1.
Departamento de Matemática Aplicada, IME-USP, Rua Do Matão 1010, Cidade Universitária, 05508-090 São Paulo SP
2.
Department of Mathematical Sciences, University of Liverpool, Liverpool L69 7ZL

Received: May 31, 2009

Revised: August 31, 2009

Published: August 2010

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Abstract

The Decoration Conjecture describes the structure of the set of braid types of Smale's horseshoe map ordered by forcing, providing information about the order in which periodic orbits can appear when a horseshoe is created. A proof of this conjecture is given for the class of so-called lone decorations, and it is explained how to calculate associated braid conjugacy invariants which provide additional information about forcing for horseshoe braids.

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Mathematics Subject Classification: Primary: 37E30, 37E15, 37B10, 37B40.

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