Related papers: Absolute continuity of complex Bernoulli convoluti…

We prove that for Bernoulli percolation on a graph $\mathbb{Z}^2\times\{0,\dots,k\}$ ($k\ge 0$), there is no infinite cluster at criticality, almost surely. The proof extends to finite range Bernoulli percolation models on $\mathbb{Z}^2$…

We consider infinitely convolved Bernoulli measures (or simply Bernoulli convolutions) related to the $\beta$-numeration. A matrix decomposition of these measures is obtained in the case when $\beta$ is a PV number. We also determine their…

We show that there is a transcendental meromorphic function with an invariant Baker domain $U$ such that every singular value of $f$ is a super-attracting periodic point. This answers a question of Bergweiler from 1993. We also show that…

In a recent paper [Adv. Math. 305:165--196, 2017], Komornik et al.~proved a long-conjectured formula for the Hausdorff dimension of the set $\mathcal{U}_q$ of numbers having a unique expansion in the (non-integer) base $q$, and showed that…

The main results of this paper are twofold: the first one is a matrix theoretical result. We say that a matriz is superregular if all of its minors that are not trivially zero are nonzero. Given a a times b, a larger than or equal to b,…

We prove almost Lipshitz continuity of spectra of singular quasiperiodic Jacobi matrices and obtain a representation of the critical almost Mathieu family that has a singularity. This allows us to prove that the Hausdorff dimension of its…

A key property of an algebraic variety is whether it is absolutely irreducible, meaning that it remains irreducible over the algebraic closure of its defining field, and determining absolute irreducibility is important in algebraic geometry…

In this note, it is proved the existence of an infinitely generated multiplicative group consisting of entire functions that are, except for the constant function 1, hypercyclic with respect to the convolution operator associated to a given…

We introduce a unified geometric framework for domains satisfying a geometric normal property (C-GNP) relative to a strictly convex set \(C\). Under the fundamental assumption that the source \(f\) is supported within the core \(C\), we…

We consider the Bernoulli bond percolation process (with parameter $p$) on infinite graphs and we give a general criterion for bounded degree graphs to exhibit a non-trivial percolation threshold based either on a single isoperimetric…

A closed interval and circle are the only smooth Julia sets in polynomial dynamics. D. Ruelle proved that the Hausdorff dimension of unicritical Julia sets close to the circle depends analytically on the parameter. Near the tip of the…

For a certain parametrized family of maps on the circle, with critical points and logarithmic singularities where derivatives blow up to infinity, a positive measure set of parameters was constructed in [19], corresponding to maps which…

In this paper we introduce probability-preserving convolution algebras on cones of positive semidefinite matrices over one of the division algebras $\b F = \b R, \b C$ or $\b H$ which interpolate the convolution algebras of radial bounded…

We study the topological, dynamical, and descriptive set theoretic properties of Hurwitz continued fractions. Hurwitz continued fractions associate an infinite sequence of Gaussian integers to every complex number which is not a Gaussian…

We consider standard and extended CMV matrices with small quasi-periodic Verblunsky coefficients and show that on their essential spectrum, all spectral measures are purely absolutely continuous. This answers a question of Barry Simon from…

This paper deals with both complex dynamical systems and conformal iterated function systems. We study finitely generated expanding semigroups of rational maps with overlaps on the Riemann sphere. We show that if a $d$-parameter family of…

We prove that the Ahlfors regular conformal dimension is upper semicontinuous with respect to Gromov-Hausdorff convergence when restricted to the class of uniformly perfect, uniformly quasi-selfsimilar metric spaces. Moreover we show the…

In this note we consider the Hausdorff dimension of self-affine sets with random perturbations. We extend previous work in this area by allowing the random perturbation to be distributed according to distributions with unbounded support as…

We prove that subharmonic functions of finite order on finite dimensional real space, bounded from above outside of some asymptotically small sets on spheres, are bounded from above everywhere. It follows that subharmonic functions of…

For the universal isomonodromic deformation of an irreducible logarithmic rank two connection over a smooth complex projective curve of genus at least two, consider the family of holomorphic vector bundles over curves underlying this…