M . Ratner's theorem on the rigidity of horocycle flows is extended to the rigidity of horospherical foliations on bundles over finite-volume locally-symmetric spaces of non-positive sectional curvature, and to other foliations of the same algebraic form.

Under explicit diophantine conditions on (α, β) ∈ R2, we prove that the local two-point correlations of the sequence given by the values (m − α)2 + (n−β)2, with (m,n) ∈ Z2, are those of a Poisson process. This partly confirms a conjecture of Berry and Tabor [2] on spectral statistics of quantized integrable systems, and also establishes a particular case of the quantitative version of the Oppen...

294/5545/1317. [3] C. Joachim and M. A. Ratner, Nanotechnology 15, 1065 (2004), URL http://stacks.iop.org/0957-4484/

A set Y ⊆ R that intersects every convex set of volume 1 is called a Danzer set. It is not known whether there are Danzer sets in R with growth rate O(T ). We prove that natural candidates, such as discrete sets that arise from substitutions and from cut-and-project constructions, are not Danzer sets. For cut and project sets our proof relies on the dynamics of homogeneous flows. We consider a ...

Bottomland hardwood forests of the southeastern United States have declined in extent since European settlement. Forest restoration activities over the past decade, however, have driven recent changes in land use through an intensified afforestation effort on former agricultural land. This intense afforestation effort, particularly in the Lower Mississippi Alluvial Valley, has generated a deman...

An afforestation system which utilizes the pioneer species eastern cottonwood (Populus deltoides Bartr. ex Marsh.) as a nurse for slower growing, disturbance-dependent species is under evaluation as a forest rehabilitation tool on former agricultural land in the Lower Mississippi River Alluvial Valley, USA. The primary objectives of this study were to quantify understory light availability in t...