Elsevier

Topology

Volume 43, Issue 2, March 2004, Pages 247-287
Topology

Braid forcing and star-shaped train tracks

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Abstract

Global results are proved about the way in which Boyland's forcing partial order organizes a set of braid types: those of periodic orbits of Smale's horseshoe map for which the associated train track is a star. This is a special case of a conjecture introduced in de Carvalho and Hall (Exp. Math. 11(2) (2002) 271), which claims that forcing organizes all horseshoe braid types into linearly ordered families which are, in turn, parameterized by homoclinic orbits to the fixed point of code 0.

MSC

37E30
37E25
37E15
37B10

Keywords

Train tracks
Braid type
Forcing
Horseshoe

Cited by (0)

1

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