Quantitative recurrence and hyperbolicity for the Teichmüller flow.
Ian Frankel (Toronto)
Monday 1st April, 2019 16:00-17:00 Maths 311B
Abstract
We will explain how quantitatively recurrent geodesics for the Teichmüller metric on the moduli space of Riemann surfaces behave like geodesics in a negatively curved space. More precisely,
Let
be the family of quadratic differentials corresponding to a length
segment of a Teichmüller geodesic, parametrized by the metric. Let
be a compact subset of the moduli space of Riemann surfaces. If the set of times
for which
belongs to
has measure at least
, and contains
and
, we will explain why the unit neighborhood of
in its strongly stable leaf is contracted by
in some metric, where the constants
depend on
and
but not
.
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