The boundary of a fibered face of the magic 3-manifold and the asymptotic behavior of the minimal pseudo-Anosovs dilatations
Abstract
Let
δ
g,n
be the minimal dilatation of pseudo-Anosovs defined on an orientable surface of genus
g
with
n
punctures. Tsai proved that for any fixed
g≥2
, the logarithm of the minimal dilatation
log
δ
g,n
is on the order of
logn
n
. The main result of this paper is that if
2g+1
is relatively prime to
s
or
s+1
for each
0≤s≤g
, then
lim sup
n→∞
nlog
δ
g,n
logn
≤2.