Dmitry Kleinbock

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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.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…