Period functions for Maass cusp forms for Γ0(p)\Gamma_0(p): a transfer operator approach

We characterize the Maass cusp forms for Hecke congruence subgroups of prime level as 1-eigenfunctions of a finite-term transfer operator.Comment: 17 pages, 6 figure

Amount of failure of upper-semicontinuity of entropy in noncompact rank one situations, and Hausdorff dimension

Recently, Einsiedler and the authors provided a bound in terms of escape of mass for the amount by which upper-semicontinuity for metric entropy fails for diagonal flows on homogeneous spaces $\Gamma\backslash G$, where $G$ is any connected semisimple Lie group of real rank 1 with finite center and $\Gamma$ is any nonuniform lattice in $G$. We show that this bound is sharp and apply the methods used to establish bounds for the Hausdorff dimension of the set of points which diverge on average.Comment: 24 page

Experimental evidence of accelerated energy transfer in turbulence

We investigate the vorticity dynamics in a turbulent vortex using scattering of acoustic waves. Two ultrasonic beams are adjusted to probe simultaneously two spatial scales in a given volume of the flow, thus allowing a dual channel recording of the dynamics of coherent vorticity structures. Our results show that this allows to measure the average energy transfer time between different spatial length scales, and that such transfer goes faster at smaller scales.Comment: 5 pages, 5 figure

Period Functions for Maass Cusp Forms for Γ0(p): A Transfer Operator Approach

We characterize Maass cusp forms for Hecke congruence subgroups of prime level as 1-eigenfunctions of a finite-term transfer operato

Ford fundamental domains in symmetric spaces of rank one

We show the existence of isometric (or Ford) fundamental regions for a large class of subgroups of the isometry group of any rank one Riemannian symmetric space of noncompact type. The proof does not use the classification of symmetric spaces. All hitherto known existence results of isometric fundamental regions and domains are essentially subsumed by our work.Comment: 54 pages; typos correcte