A family of pseudo-Anosov braids with small dilatation
Eriko Hironaka and Eiko Kin

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 $\log(2 + \sqrt{3})/g$.   By taking double covers,
we obtain pseudo-Anosov mapping classes on genus g surfaces with 
smallest known dilatation, and improve on Penner and Bauer's upper
bounds.