arXiv subjects

Shirali Kadyrov

Publications and source records attributed to Shirali Kadyrov.

23 records · Page 2Linked to original sources

arXiv2012

Amount of failure of upper-semicontinuity of entropy in noncompact rank one situations, and Hausdorff dimension

Recently, Einsiedler and the authors provided a bound in terms of escape of mass for the amount by which upper-semicontinuity for metric entropy fails for diagonal flows on homogeneous spaces $Γ\backslash G$, where $G$ is any connected semisimple Lie group of real rank 1 with finite center and $Γ$ is any nonuniform lattice in $G$. We show that this bound is sharp and apply the methods used to establish bounds for the Hausdorff dimension of the set of points which diverge on average.

math.DS↗

arXiv2011

Entropy and Escape of Mass for Hilbert Modular Spaces

We study the relation between metric entropy and escape of mass for the Hilbert modular spaces with the action of a diagonal element.

math.DS↗

arXiv2011

Algebraic Numbers, Hyperbolicity, and Density Modulo One

We prove the density of the sets of the form ${λ_1^m μ_1^n ξ_1 +...+λ_k^m μ_k^n ξ_k : m,n \in \mathbb N}$ modulo one, where $λ_i$ and $μ_i$ are multiplicatively independent algebraic numbers satisfying some additional assumptions. The proof is based on analysing dynamics of higher-rank actions on compact abelean groups.

math.DS↗

arXiv2010

Positive Entropy Invariant Measures on the Space of Lattices with Escape of Mass

On the space of unimodular lattices, we construct a sequence of invariant probability measures under a singular diagonal element with high entropy and show that the limit measure is 0.

math.DS↗

arXiv2010

Entropy and escape of mass for $SL(3,Z)\SL(3,R)$

We study the relation between measure theoretic entropy and escape of mass for the case of a singular diagonal flow on the moduli space of three-dimensional unimodular lattices.

math.DS↗