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August  2010, 27(3): 863-906. doi: 10.3934/dcds.2010.27.863

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, Brazil
2. 

Department of Mathematical Sciences, University of Liverpool, Liverpool L69 7ZL, United Kingdom

Received  June 2009 Revised  September 2009 Published  March 2010

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.
Keywords: Forcing relations, Horseshoe, Decoration conjecture..
Mathematics Subject Classification: Primary: 37E30, 37E15, 37B10, 37B4.
Citation: André de Carvalho, Toby Hall. Decoration invariants for horseshoe braids. Discrete & Continuous Dynamical Systems - A, 2010, 27 (3) : 863-906. doi: 10.3934/dcds.2010.27.863
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