Ronggang Shi

activity

20092025

most citedHausdorff dimension of divergent trajectories on homogeneous space

9 citations · 33 across the 15 of their papers we have counts for

collaborators

19 papers

math.DS2025

Bounded diagonal orbits in homogeneous spaces over function fields

Qianlin Huang, Ronggang Shi

This paper is about topological rigidity of diagonal group actions on the homogeneous $\SL_4\big(\F(\!(t^{-1})\!)\big)/\SL_4(\F[t])$ where $\F$ is a finite field of characteristic…

math.NT2024

The Product of linear forms over function fields

Wenyu Guo, Xuan Liu, Ronggang Shi

The aim of this paper is to study the product of $n$ linear forms over function fields. We calculate the maximum value of the minima of the forms with determinant one when $n$ is s…

math.DS2021★ 6 cited

Expanding measures: Random walks and rigidity on homogeneous spaces

Roland Prohaska, Cagri Sert, Ronggang Shi

Let $G$ be a real Lie group, $Λ < G$ a lattice and $H < G$ a connected semisimple subgroup without compact factors and with finite center. We define the notion of $H$ -expanding measure…

math.DS2020★ 2 cited

Divergent trajectories on products of homogeneous spaces

Jinpeng An, Lifan Guan, Antoine Marnat +1

In this paper, we determine the Hausdorff dimension of the set of points with divergent trajectories on the product of certain homogeneous spaces. The flow is allowed to be weighte…

math.DS2019★ 1 cited

Quantitative Multiple pointwise convergence and effective multiple correlations

Rene Rühr, Ronggang Shi

We show that effective $2 ℓ$ -multiple correlations imply quantitative $ℓ$ -multiple pointwise ergodic theorems. The result has a wide class of applications which include subgro…

math.NT2019★ 1 cited

Metric Diophantine approximation with congruence conditions

Erez Nesharim, Rene Rühr, Ronggang Shi

We prove a version of the Khinchine--Groshev theorem for Diophantine approximation of matrices subject to a congruence condition. The proof relies on an extension of the Dani corre…

math.DS2018

Central Limit theorem and cohomological equation on homogeneous spaces

Ronggang Shi

The dynamics of one parameter diagonal group actions on finite volume homogeneous spaces has a partially hyperbolic feature. In this paper we extend the Livšic type result to these…

math.DS2018★ 9 cited

Hausdorff dimension of divergent trajectories on homogeneous space

Lifan Guan, Ronggang Shi

For one parameter subgroup action on a finite volume homogeneous space, we consider the set of points admitting divergent on average trajectories. We show that the Hausdorff dimens…

math.DS2017

Measure rigidity for solvable group actions in the space of lattices

Manfred Einsiedler, Ronggang Shi

We study invariant probability measures on the homogeneous space $SL_{n} (R) / SL_{n} (Z)$ for the action of subgroups of $SL_{n} (R)$ of th…

math.DS2016★ 1 cited

Hausdorff dimension of weighted singular vectors

Lingmin Liao, Ronggang Shi, Omri N. Solan +1

Let $w = (w_{1}, w_{2})$ be a pair of positive real numbers with $w_{1} + w_{2} = 1$ and $w_{1} \geq w_{2}$ . We show that the set of $w$ -weighted singular vectors in $R^{2}$ has Hausdorff dimens…

math.DS2015★ 6 cited

Expanding cone and applications to homogeneous dynamics

Ronggang Shi

Let $U$ be a horospherical subgroup of a noncompact simple Lie group $H$ and let $A$ be a maximal split torus in the normalizer of $U$ . We define the expanding cone $A_{U}^{+}$ in $A$ …

math.DS2015

Genericity on curves and applications: pseudo-integrable billiards, Eaton lenses and gap distributions

Krzysztof Frączek, Ronggang Shi, Corinna Ulcigrai

In this paper we prove results on Birkhoff and Oseledets genericity along certain curves in the space of affine lattices and in moduli spaces of translation surfaces. We also prove…

math.DS2015

Pointwise equidistribution with an error rate and with respect to unbounded functions

Dmitry Kleinbock, Ronggang Shi, Barak Weiss

Consider $G=\SL_{ d }(\mathbb R)$ and $ Γ=\SL_{ d }(\mathbb Z)$. It was recently shown by the second-named author \cite{s} that for some diagonal subgroups ${g_{t}} \subset G$ and u…

math.DS2014★ 1 cited

Invariant measures for solvable groups and diophantine approximation

Ronggang Shi, Barak Weiss

We show that if $L$ is a line in the plane containing a badly approximable vector, then almost every point in $L$ does not admit an improvement in Dirichlet's t…

math.DS2014

Simultaneous dense and nondense orbits and the space of lattices

Ronggang Shi, Jimmy Tseng

We show that set of points nondense under the $\times n$ -map on the circle and dense for the geodesic flow under the induced map on the circle corresponding to the expanding horosp…

math.DS2014★ 3 cited

Pointwise equidistribution for one parameter diagonalizable group action on homogeneous space

Ronggang Shi

Let $Γ$ be a lattice of a semisimple Lie group $L$ . Suppose that one parameter Ad-diagonalizable subgroup ${g_{t}}$ of $L$ acts ergodically on $L /Γ$ with respect to the probability…

math.DS2011

S-adic version of Minkowski's geometry of numbers and Mahler's compactness criterion

Dmitry Kleinbock, Ronggang Shi, George Tomanov

In this note we give a detailed proof of certain results on geometry of numbers in the $S$ -adic case. These results are well-known to experts, so the aim here is to provide a conve…

math.DS2011

Convergence of measures under diagonal actions on homogeneous spaces

Ronggang Shi

Let $λ$ be a probability measure on $T^{n - 1}$ where $n = 2$ or 3. Suppose $λ$ is invariant, ergodic and has positive entropy with respect to the linear transformation defined…

math.DS2009★ 3 cited

Equidistribution of expanding measures with local maximal dimension and Diophantine Approximation

Ronggang Shi

We consider improvements of Dirichlet's Theorem on space of matrices $M_{m, n} (R)$ . It is shown that for a certain class of fractals $K \subset [0, 1]^{mn} \subset M_{m, n} (R)$ of local…