Invariant distributions and time averages for horocycle flows

By L. Flaminio, G. Forni. 2003

193 citations recorded by the source corpus.

Subfields: Applied Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/b6cae26f73abd8203b3d7d8fbd3af9c532778c5b

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In Applied Mathematics

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Chapter 11 Spectral properties and combinatorial constructions in ergodic theory (2006, unknown): “Cohomological equations over the horocycle flows has been throughly studied by Flaminio and Forni in [53]; see [78, Section 11.”
A Poincar\'e section for horocycle flow on the space of lattices (2012, background): “Flaminio-Forni [17] and Strömbergsson [34] have proved essentially optimal results for the deviation of ergodic averages for hs on X2.”
Equidistribution of nilflows and applications to theta sums (2006, methodology): “As in the case of generic flows on surfaces of higher genus [For02b] and of horocycle flows on surfaces of constant negative curvature [ FF03 ], we have that the equidistribution of a generic nilflow obeys a power law with respect to time, whose exponents are determined by the Lyapunov spectrum of a”
ON THE DEVIATION OF ERGODIC AVERAGES FOR HOROCYCLE FLOWS (2013, methodology): “[4] A. Bufetov and G. Forni, Limit theorems for horocycle flows, arXiv:1104.4502.”
Limit theorems for translation flows (2008, methodology): “For horocycle flows on compact surfaces of constant negative curvature, compactness of support for all weak accumulation points of ergodic integrals has been obtained by Flaminio and Forni [19].”
Effective equidistribution for closed orbits of semisimple groups on homogeneous spaces (2007, background): “More detailed analysis of the quantitative equidistribution of the horocycle flow for SL2(R) may be found in [23, 60]; quantitative mixing rates are discussed in [26], and analysis of equidistribution of closed horospheres and its relevance to the theory of automorphic forms may be found in [61].”