26 citations · 69 across the 10 of their papers we have counts for
11 papers
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…
On rigidity properties of time-changes of unipotent flows
Mauro Artigiani, Livio Flaminio, Davide Ravotti
We study time-changes of unipotent flows on finite volume quotients of semisimple linear groups, generalising previous work by Ratner on time-changes of horocycle flows. Any measur…
Abelian covers of hyperbolic surfaces: equidistribution of spectra and infinite volume mixing asymptotics for horocycle flows
Livio Flaminio, Davide Ravotti
We consider Abelian covers of compact hyperbolic surfaces. We establish an asymptotic expansion of the correlations for the horocycle flow on -covers, thus proving a…
Orthogonal powers and Möbius conjecture for smooth time changes of horocycle flows
Livio Flaminio, Giovanni Forni
We derive, from the work of M. Ratner on joinings of time-changes of horocycle flows and from the result of the authors on its cohomology, the property of orthogonality of powers f…
Approximate orthogonality of powers for ergodic affine unipotent diffeomorphisms on nilmanifolds
Livio Flaminio, Krzysztof Frączek, Joanna Kułaga-Przymus +1
Let be a connected, simply connected nilpotent Lie group and a lattice. We prove that each ergodic diffeomorphism on the nilmanifold , where $…
Effective equidistribution of twisted horocycle flows and horocycle maps
Livio Flaminio, Giovanni Forni, James Tanis
We prove bounds for twisted ergodic averages for horocycle flows of hyperbolic surfaces, both in the compact and in the non-compact finite area case. From these bounds we derive ef…
Equidistribution for higher-rank Abelian actions on Heisenberg nilmanifolds
Salvatore Cosentino, Livio Flaminio
We prove quantitative equidistribution results for actions of Abelian subgroups of the dimensional Heisenberg group acting on compact -dimensional homogeneous nilmanif…
On effective equidistribution for higher step nilflows
Livio Flaminio, Giovanni Forni
The main goal of this paper is to obtain optimal estimates on the speed of equidistribution of nilflows on higher step nilmanifolds. Under a Diophantine condition on the frequencie…
Invariant Distributions for homogeneous flows
Livio Flaminio, Giovanni Forni, Federico Rodriguez Hertz
We prove that every homogeneous flow on a finite-volume homogeneous manifold has countably many independent invariant distributions unless it is conjugate to a linear flow on a tor…
Linearization of Cohomology-free Vector Fields
Livio Flaminio, Miguel Paternain
We study the cohomological equation for a smooth vector field on a compact manifold. We show that if the vector field is cohomology free, then it can be embedded continuously in a…
On the cohomological equation for nilflows
Livio Flaminio, Giovanni Forni
Let X be a vector field on a compact connected manifold M. An important question in dynamical systems is to know when a function g:M -> R is a coboundary for the flow generated by…