2 citations · 4 across the 7 of their papers we have counts for
10 papers
Exact logarithmic Hausdorff and capacity exponents of the non-Brjuno set
Sardor Bazarbaev, Karim Rakhimov
Let be the set of non-Brjuno real numbers. We determine the exact critical exponent of for both logarithmic Hausdorff measure and logarithmic capacity.…
Linear response for random systems with a cusp
Davrbek Oltiboev, Karim Rakhimov, Marks Ruziboev
We study i.i.d.\ random compositions of cusp tent-like interval maps having a common cusp point and a common cusp value. For cusp exponents , we prove that the assoc…
On the support of measures of large entropy for automorphisms of Kähler manifolds
Fabrizio Bianchi, Sobir Boymurodov, Karim Rakhimov
Let be a holomorphic automorphism of a compact Kähler manifold with simple action on cohomology. We show that every ergodic measure with sufficiently large entropy is suppo…
On the support of measures of large entropy for polynomial-like maps
Sardor Bazarbaev, Fabrizio Bianchi, Karim Rakhimov
Let be a polynomial-like map with dominant topological degree and let be its dynamical degree of order . We show that the support of every ergodi…
Hölder continuity and laminarity of the Green currents for Hénon-like maps
Fabrizio Bianchi, Tien-Cuong Dinh, Karim Rakhimov
Under a natural assumption on the dynamical degrees, we prove that the Green currents associated to any Hénon-like map in any dimension have Hölder continuous super-potentials, i.e…
Dynamics of Fuchsian meromorphic connections with real periods
Marco Abate, Karim Rakhimov
In this paper, we study the dynamics of geodesics of Fuchsian meromorphic connections with real periods, giving a precise characterization of the possible -limit sets of simple…
Monotonicity of dynamical degrees for H{é}non-like and polynomial-like maps
Fabrizio Bianchi, Tien-Cuong Dinh, Karim Rakhimov
We prove that, for every invertible horizontal-like map (i.e., H{é}non-like map) in any dimension, the sequence of the dynamical degrees is increasing until that of maximal value,…
Strong probabilistic stability in holomorphic families of endomorphisms of and polynomial-like maps
Fabrizio Bianchi, Karim Rakhimov
We prove that, in stable families of endomorphisms of , all invariant measures whose measure-theoretic entropy is strictly larger than at a…
A mean value criterion for plurisubharmonic functions
Karim Rakhimov, Shomurod Shopulatov
In this paper we prove a criterion for plurisubharmonic functions in terms of integral mean by complex ellipsoids. Moreover, by using the criterion we prove an analogue of Blaschke…
Flat structure of meromorphic connections on Riemann surfaces
Karim Rakhimov
The possible omega limit sets of simple geodesics for meromorphic connections on compact Riemann surfaces have been studied by Abate, Tovena and Bianchi. In this paper, we study th…