Dmitry Kleinbock

collaborators

6 papers

math.DS2026

Bounded trajectories of quasi-rays on homogeneous spaces and Diophantine approximation with weight functions

Dmitry Kleinbock, Vasiliy Neckrasov

Let $G$ be a connected semisimple real Lie group, $I^$ an irreducible lattice in $G$ and $X = G / I^$ . Let $F = {g_{t} : t \geq 0}$ be a non-quasiunipotent one-parameter subsemigroup of…

math.NT2026

Uniform Diophantine approximation with restrictions via total density of collections of subspaces

Leo Hong, Dmitry Kleinbock, Vasiliy Neckrasov

In 1926 Khintchine introduced a topological argument proving the existence of uncountably many nontrivial singular linear forms of $n \geq 2$ variables. Throughout the years, this…

math.DS2026

Constructing bounded orbits of special types on homogeneous spaces

Manfred Einsiedler, Dmitry Kleinbock, Anurag Rao

Let $X = G / I^$ be a quotient of a real Lie group by a non-uniform lattice. Consider a one-parameter subgroup $F$ of $G$ that is $Ad$ -diagonalizable over $C$ …

math.DS2025

Simultaneously bounded and dense orbits for commuting Cartan actions

Dmitry Kleinbock, Chengyang Wu

In this paper we prove that the set of points that have bounded orbits under one regular diagonal flow and dense orbits under the other diagonal flow commuting with the first one h…

math.NT2025

Singularity, weighted uniform approximation, intersections and rates

Dmitry Kleinbock, Nikolay Moshchevitin, Jacqueline Warren +1

A classical argument was introduced by Khintchine in 1926 in order to exhibit the existence of totally irrational singular linear forms in two variables. This argument was subseque…

math.NT2025

Submanifold-genericity of $R^{d}$ -actions and uniform multiplicative Diophantine approximation

Prasuna Bandi, Reynold Fregoli, Dmitry Kleinbock

In this paper, we prove a new ergodic theorem for $R^{d}$ -actions involving averages over dilated submanifolds, thereby generalizing the theory of spherical averages. Our ma…