Logarithmic suspension flows over interval exchange transformations
Corinna ULCIGRAI (PRINCETON)

We consider suspension flows over interval exchange transformations (IETs), under a roof function with logarithmic singularities. As a motivation, such flows arise as minimal components of flows on surfaces given by multi-valued Hamiltonians.

We prove that if the roof function has an asymmetric logarithmic singularity, the suspension flow is mixing for a full measure set of IETs. If the singularity is symmetric, we show weak mixing for a full measure set of IETs and absence of mixing for a special class of IETs. The key ingredients in both cases are estimates on the growth rate of Birkhoff sums of a non integrable function.