Shahriar Mirzadeh

activity

20172023

collaborators

5 papers

math.DS2023

Dimension bounds for escape on average in homogeneous spaces

Dmitry Kleinbock, Shahriar Mirzadeh

Let $X = G /Γ$ , where $G$ is a Lie group and $Γ$ is a uniform lattice in $G$ , and let $O$ be an open subset of $X$ . We give an upper estimate for the Hausdorff dimension of the set…

math.DS2022

Dimension drop for diagonalizable flows on homogeneous spaces

Dmitry Kleinbock, Shahriar Mirzadeh

Let $X = G /Γ$ , where $G$ is a Lie group and $Γ$ is a lattice in $G$ , let $O$ be an open subset of $X$ , and let $F = {g_{t} : t \geq 0}$ be a one-parameter subsemigroup of $G$ . Conside…

math.DS2020

On the dimension drop conjecture for diagonal flows on the space of lattices

Dmitry Kleinbock, Shahriar Mirzadeh

Let $X = G /Γ$ , where $G$ is a Lie group and $Γ$ is a lattice in $G$ , let $U$ be an open subset of $X$ , and let ${g_{t}}$ be a one-parameter subgroup of $G$ . Consider the set of poi…

math.DS2017

Exceptional directions for the Teichmüller geodesic flow and Hausdorff dimension

Hamid Al-Saqban, Paul Apisa, Alena Erchenko +3

We prove that for every flat surface $ω$ , the Hausdorff dimension of the set of directions in which Teichmüller geodesics starting from $ω$ exhibit a definite amount of deviation f…

math.DS2017

Dimension estimates for the set of points with non-dense orbit in homogeneous spaces

Dmitry Kleinbock, Shahriar Mirzadeh

Let $X = G /Γ$ , where $G$ is a Lie group and $Γ$ is a lattice in $G$ , and let $U$ be a subset of $X$ whose complement is compact. We use the exponential mixing results for diagonali…