A family of pseudo-Anosov braids with small dilatation

dc.creatorHironaka, Eriko
dc.creatorKin, Eiko
dc.date2005-07-01
dc.date.accessioned2026-07-07T05:21:18Z
dc.date.available2026-07-07T05:21:18Z
dc.descriptionThis paper concerns a family of pseudo-Anosov braids with dilatations arbitrarily close to one. The associated graph maps and train tracks have stable "star-like" shapes, and the characteristic polynomials of their transition matrices form Salem-Boyd sequences. These examples show that the logarithms of least dilatations of pseudo-Anosov braids on $2g+1$ strands are bounded above by $\log(2 + \sqrt{3})/g$. It follows that the asymptotic behavior of least dilatations of pseudo-Anosov, hyperelliptic surface homeomorphisms is identical to that found by Penner for general surface homeomorphisms. The family includes pseudo-Anosov braids with minimum dilatation for 3,4, and 5 strands; the latter according to a recent anouncement of J.-Y. Ham and W.-T. Song [math.GT/0506295].
dc.description38 pages, 28 figures
dc.identifierhttps://arxiv.org/abs/math/0507012
dc.identifierhttp://arxiv.org/abs/math/0507012
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/75640
dc.subjectGeometric Topology
dc.subjectDynamical Systems
dc.subject37E30; 57M50
dc.titleA family of pseudo-Anosov braids with small dilatation
dc.typetext

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