A family of pseudo-Anosov braids with small dilatation
| dc.creator | Hironaka, Eriko | |
| dc.creator | Kin, Eiko | |
| dc.date | 2005-07-01 | |
| dc.date.accessioned | 2026-07-07T05:21:18Z | |
| dc.date.available | 2026-07-07T05:21:18Z | |
| dc.description | This 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.description | 38 pages, 28 figures | |
| dc.identifier | https://arxiv.org/abs/math/0507012 | |
| dc.identifier | http://arxiv.org/abs/math/0507012 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/75640 | |
| dc.subject | Geometric Topology | |
| dc.subject | Dynamical Systems | |
| dc.subject | 37E30; 57M50 | |
| dc.title | A family of pseudo-Anosov braids with small dilatation | |
| dc.type | text |