33 citations · 199 across the 33 of their papers we have counts for
40 papers
Existence of a Periodic Orbit for Billiards in Polygons
Giovanni Forni
We prove that the billiard flow in any finite polygon has at least one periodic orbit. The proof by contradiction is based on a fundamental result on the dynamics of the billiard f…
Infinitesimal random dynamics of certain Veech groups on SU(2)-character varieties
Giovanni Forni, William M. Goldman, Sean Lawton +1
Almost 20 years ago, the first and fourth authors found examples of SL(2,R)-invariant subbundles of Hodge bundles over Teichmüller curves having maximally degenerate Lyapunov spect…
Equidistribution of nilflows and bounds on Weyl sums
Livio Flaminio, Giovanni Forni
We prove an effective equidistribution result for a class of higher step nilflows, called filiform nilflows, and derive bounds on Weyl sums for higher degree polynomials with a pow…
A Central Limit Theorem for the Kontsevich-Zorich Cocycle
Hamid Al-Saqban, Giovanni Forni
We show that a central limit theorem holds for exterior powers of the Kontsevich-Zorich (KZ) cocycle. In particular, we show that, under the hypothesis that the top Lyapunov expone…
Non-ergodicity on SU(2) and SU(3) character varieties of the once-punctured torus
Giovanni Forni, William Goldman, Sean Lawton +1
Utilizing KAM theory, we show that there are certain levels in relative SU(2) and SU(3) character varieties of the once-punctured torus where the action of a single hyperbolic elem…
Counterexamples to a rigidity conjecture
Giovanni Forni, Adam Kanigowski
We discuss several counterexamples to a rigidity conjecture of K. Khanin, which states that under some quantitative condition on non-existence of periodic orbits, conjugacy i…