Affiliation:
1. Mathematisches Institut der Universität Bonn , Endenicher Allee 60, 53115 Bonn , Germany
Abstract
Abstract
Let S be a closed oriented surface of
genus
g
≥
0
{g\geq 0}
with
n
≥
0
{n\geq 0}
punctures and
3
g
-
3
+
n
≥
5
{3g-3+n\geq 5}
.
Let
𝒬
{{\mathcal{Q}}}
be a connected component
of a stratum in the moduli space
𝒬
(
S
)
{{\mathcal{Q}}(S)}
of area one
meromorphic quadratic differentials on S with n
simple poles at the punctures
or in the moduli space
ℋ
(
S
)
{{\mathcal{H}}(S)}
of abelian differentials on S if
n
=
0
{n=0}
.
For a compact subset K of
𝒬
(
S
)
{{\mathcal{Q}}(S)}
or of
ℋ
(
S
)
{{\mathcal{H}}(S)}
,
we show that the asymptotic growth rate of the number of periodic orbits for the
Teichmüller flow
Φ
t
{\Phi^{t}}
on
𝒬
{{\mathcal{Q}}}
which are entirely contained in
𝒬
-
K
{{\mathcal{Q}}-K}
is at least
h
(
𝒬
)
-
1
{h({\mathcal{Q}})-1}
,
where
h
(
𝒬
)
>
0
{h({\mathcal{Q}})>0}
is the complex dimension of
ℝ
+
𝒬
{\mathbb{R}^{+}{\mathcal{Q}}}
.
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