Unique ergodicity is generally implied by some form of
recurrence.
For example, a result of Masur asserts that a measured foliation is
uniquely
ergodic if the associated Teichm\"uller geodesic ray is recurrent when
projected
to moduli space. The converse is not true in general--there are are
uniquely
ergodic measured foliations associated to divergent Teichm\"uller
geodesic.
In this talk, I will discuss general conditions under which a slowly
divergent
Teichm\"uller geodesic is necessarily determined by a uniquely ergodic
measured foliation. This is joint work with Alex Eskin.

Lecture #12600

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