Multiple mixing for area preserving flows
speaker: Corinna Ulcigrai (University of Bristol)abstract: In joint work with Adam Kanigowski and Joanna Julaga-Prysmus, we consider smooth area preserving flows on surfaces of higher genus (also known as locally Hamiltonian flows). We show that the typical such flow (in the measure theoretical sense) which has several mixing minimal components, is actually mixing of all orders when restricted to each minimal component (thus verifying Rohlin's conjecture that mixing implies mixing of all orders in this context). In this talk we will first recall and explain the basic mechanism of shearing which has proved key in proving mixing of several classes of parabolic dynamical systems.The proof of multiple mixing exploits quantitative shearing estimates (in the form of a variant of the Ratner property recently introduced by Fayad and Kanigowski to prove an analogous result in the genus one case). We will explain how the underlying hyperbolic renormalization dynamics (given by the Teichmueller geodesic flow or Rauzy-Veech induction) is key to provide Diophantine-like conditions under which the result on area preserving flows holds.
timetable:
Fri 1 Jul, 10:15 - 11:00, Aula Dini
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