33 citations · 43 across the 6 of their papers we have counts for
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An example of a Teichmuller disk in genus 4 with degenerate Kontsevich-Zorich spectrum
Giovanni Forni, Carlos Matheus
We construct an orientable holomorphic quadratic differential on a Riemann surface of genus 4 whose SL(2,R)-orbit is closed and has a highly degenerate Kontsevich - Zorich spectrum…
On the Greenfield-Wallach and Katok conjectures
Giovanni Forni
We survey recent progress on the Greenfield-Wallach and Katok conjectures on globally hypoelliptic and cohomology free vector fields and derive a proof of the conjectures in dimens…
Deviation of ergodic averages for rational polygonal billiards
Jayadev S. Athreya, Giovanni Forni
We prove polynomial upper bounds for the deviation of ergodic averages for the straight line flow on every translation surface in almost every direction, in particular for those su…
Weak mixing for interval exchange transformations and translation flows
Artur Avila, Giovanni Forni
We show that a typical interval exchange transformation is either weakly mixing or it is an irrational rotation. We also conclude that a typical translation flow on a surface of ge…
Deviation of ergodic averages for area-preserving flows on surfaces of higher genus
Giovanni Forni
We prove a substantial part of a conjecture of Kontsevich and Zorich on the Lyapunov exponents of the Teichmuller geodesic flow on the deviation of ergodic averages for generic con…
Asymptotic behaviour of ergodic integrals of `renormalizable' parabolic flows
Giovanni Forni
Ten years ago A. Zorich discovered, by computer experiments on interval exchange transformations, some striking new power laws for the ergodic integrals of generic non-exact Hamilt…