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Browsing Mathematics by Author "Kadyrov, Shirali"

Now showing items 1-9 of 9

Algebraic numbers, hyperbolicity, and density modulo one

Kadyrov, Shirali; Gorodnik, A. (2011)
Amount of failure of upper-semicontinuity of entropy in noncompact rank one situations, and hausdorff dimension

Kadyrov, Shirali; Pohl, A. (2012)

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 ows on homogeneous spaces 􀀀nG, where G is any connected ...
Bernstein-walsh inequalities in higherdimensions over exponential curves

Kadyrov, Shirali; Lawrence, Mark (2011)

Let x = (x1; : : : ; xd) 2 [􀀀1; 1]d be linearly independent over Z, set K = f(ez; ex1z; ex2z : : : ; exdz) : jzj 1g:We prove sharp estimates for the growth of a polynomial of degree n, in terms of En(x) := supfkPk d+1 ...
Effective uniqueness of parry measure and exceptional sets in ergodic theory

Kadyrov, Shirali (2014)

It is known that hyperbolic dynamical systems admit a unique invariant probability measure with maximal entropy. We prove an effective version of this statement and use it to estimate an upper bound for Hausdorff dimension ...
Entropy and escape of mass for SL3(Z)n SL3(R)

Einsiedler, Manfred; Kadyrov, Shirali (2011)

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
Escape of mass and entropy for diagonal flows in real rank one situations

Einsiedler, M.; Kadyrov, Shirali; Pohl, A. (2011)

Let G be a connected semisimple Lie group of real rank 1 with finite center, let 􀀀 be a non-uniform lattice in G and a any diagonalizable element in G. We investigate the relation between the metric entropy of a acting ...
Exceptional sets in homogeneous spaces and hausdorff dimension

Kadyrov, Shirali (2015)

In this paper we study the dimension of a family of sets arising in open dynamics. We use exponential mixing results for diagonalizable ows in compact homogeneous spaces X to show that the Hausdorff dimension of set of ...
Positive entropy invariant measures on the space of lattices with escape of mass

Kadyrov, Shirali (2010)

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
Singular systems of linear forms and non-escape of mass in the space of lattices

Kadyrov, Shirali; Kleinbock, D.; Lindenstrauss, E.; Margulis, G.A. (2014)

Singular systems of linear forms were introduced by Khintchine in the 1920s, and it was shown by Dani in the 1980s that they are in one-to-one correspondence with certain divergent orbits of oneparameter diagonal groups ...