Related papers: Dynamical approximation and kernels of nonescaping…

We study conjugate-type phenomena for complex-valued harmonic quasiregular mappings in the unit disk across three function space families: $Q(n,p,\alpha)$, $F(p,q,s)$, and the non-derivative $M(p,q,s)$. For a harmonic $K$-quasiregular…

We show that a family ${\cal F}$ of meromorphic functions in a domain $D$ satisfying $$\frac{|f^{(k)}|}{1+|f^{(j)}|^\alpha}(z)\ge C \qquad \mbox{for all} z\in D \mbox{and all} f\in {\cal F}$$ (where $k$ and $j$ are integers with $k>j\ge 0$…

In this note we show the characteristic function of every indecomposable set $F$ in the plane is $BV$ equivalent to the characteristic function a closed set $\mathbb{F}$, i.e.…

We build an example of a non-transitive, dynamically coherent partially hyperbolic diffeomorphism $f$ on a closed $3$-manifold with exponential growth in its fundamental group such that $f^n$ is not isotopic to the identity for all $n\neq…

For every $m\geq 2$ we produce an example of a non-hyperbolic finitely presented subgroup $H < G$ of a hyperbolic group $G$, which is the kernel of a surjective homomorphism $\phi: G\to \mathbb{Z}^m$. The examples we produce are of…

This note concerns non-autonomous dynamics of rational functions and, more precisely, the fractal behavior of the Julia sets under perturbation of non-autonomous systems. We provide a necessary and sufficient condition for holomorphic…

This paper introduces a rigorous computer-assisted procedure for analyzing hyperbolic 3-manifolds. This technique is used to complete the proof of several long-standing rigidity conjectures in 3-manifold theory as well as to provide a new…

We show that if a partially hyperbolic diffeomorphism of a Seifert manifold induces a map in the base which has a pseudo-Anosov component then it cannot be dynamically coherent. This extends work of Bonatti, Gogolev, Hammerlindl and Potrie…

We consider compact sets which are invariant and partially hyperbolic under the dynamics of a diffeomorphism of a manifold. We prove that such a set K is contained in a locally invariant center submanifold if and only if each strong stable…

This paper continues our investigation of the dynamics of families of transcendental meromorphic functions with finitely many singular values all of which are finite. Here we look at a generalization of the family of polynomials…

Let $G$ be a group hyperbolic relative to a finite collection of subgroups $\mathcal P$. Let $\mathcal F$ be the family of subgroups consisting of all the conjugates of subgroups in $\mathcal P$, all their subgroups, and all finite…

Let $G$ be a group and $\mathcal{F}$ be a family of subgroups closed under conjugation and subgroups. A model for the classifying space $E_{\mathcal{F}} G$ is a $G$-CW-complex $X$ such that every isotropy group belongs to $\mathcal{F}$, and…

Let $F$ be a field and $E$ an extension of $F$ with $[E:F]=d$ where the characteristic of $F$ is zero or prime to $d$. We assume $\mu_{d^2}\subset F$ where $\mu_{d^2}$ are the $d^2$th roots of unity. This paper studies the problem of…

We show the existence of a family of manifolds on which all (pointwise or absolutely) partially hyperbolic systems are dynamically coherent. This family is the set of 3-manifolds with nilpotent, non-abelian fundamental group. We further…

Let G be a finitely generated relatively hyperbolic group. We show that if no peripheral subgroup of G is hyperbolic relative to a collection of proper subgroups, then the fixed subgroup of every automorphism of G is relatively quasiconvex.…

We provide a new method to approximate a (possibly discontinuous) function using Christoffel-Darboux kernels. Our knowledge about the unknown multivariate function is in terms of finitely many moments of the Young measure supported on the…

In complex dynamics, the boundaries of higher dimensional hyperbolic components in holomorphic families of polynomials or rational maps are mysterious objects, whose topological and analytic properties are fundamental problems. In this…

We study dynamics in a neighborhood of a nonhyperbolic fixed point or an irreducible homoclinic tangent point. General type conditions for the existence of infinite sets of periodic points are obtained. A new method, based on the study of…

The classical Newtonian potentials, defined in terms of metrics, give rise to the basic family of kernels defining linear integral operators and posing the fundamental problems of linear harmonic analysis. When the binary character of a…

We exhibit an analytic family of hyperbolic, even disjoint type, entire functions for which the hyperbolic dimension does not vary analytically. Additionally we answer several questions in thermodynamic formalism of entire functions such as…