16 citations · 83 across the 21 of their papers we have counts for
5 papers · 2 filters
Limiting Distributions of Translates of Divergent Diagonal Orbits
Uri Shapira, Cheng Zheng
We define a natural topology on the collection of (equivalence classes up to scaling of) locally finite measures on a homogeneous space and prove that in this topology, pushforward…
Equidistribution of divergent orbits of the diagonal group in the space of lattices
Ofir David, Uri Shapira
We consider divergent orbits of the group of diagonal matrices in the space of lattices in Euclidean space. We define two natural numerical invariants of such orbits: The discrimin…
Dynamics on the space of 2-lattices in 3-space
Oliver Sargent, Uri Shapira
We study the dynamics of and its subgroups on the homogeneous space consisting of homothety classes of rank-2 discrete subgroups of . We focus…
Equidistribution of divergent orbits and continued fraction expansion of rationals
Ofir David, Uri Shapira
We establish an equidistribution result for push-forwards of certain locally finite algebraic measures in the adelic extension of the space of lattices in the plane. As an applicat…
Dimension bound for badly approximable grids
Seonhee Lim, Nicolas de Saxcé, Uri Shapira
We show that for almost any vector in , for any there exists such that the dimension of the set of vectors satisfying $\liminf_{k\to\infty} k^{1/n…