5 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…
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…