A thermodynamic formalism approach to the Selberg zeta function for Hecke triangle surfaces of infinite area

We provide an explicit construction of a cross section for the geodesic flow on infinite-area Hecke triangle surfaces which allows us to conduct a transfer operator approach to the Selberg zeta function. Further we construct closely related cross sections for the billiard flow on the associated triangle surfaces and endow the arising discrete dynamical systems and transfer operator families with two weight functions which presumably encode Dirichlet respectively Neumann boundary conditions. The Fredholm determinants of these transfer operator families constitute dynamical zeta functions, which provide a factorization of the Selberg zeta function of the Hecke triangle surfaces.Comment: 23 pages, 6 figure

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