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Browsing Mathematics by Author "Kadyrov, Shirali"
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Kadyrov, Shirali; Gorodnik, A.
(2011)
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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 ...
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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 ...
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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 ...
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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
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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 ...
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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 ...
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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
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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 ...