相关论文: The escaping set of a quasiregular mapping
We consider the evolution of a connected set on the plane carried by a periodic incompressible stochastic flow. While for almost every realization of the random flow at time t most of the particles are at a distance of order sqrt{t} away…
We give examples of closed, oriented 3-manifolds whose fundamental groups are not isomorphic, but yet have the same sets of finite quotient groups; hence the same profinite completions. We also give examples of compact, oriented 3-manifolds…
The attracting set and the inverse limit set are important objects associated to a self-map on a set. We call \emph{stable set} of the self-map the projection of the inverse limit set. It is included in the attracting set, but is not equal…
We characterize the subsets $E \subset \mathbb{R}$ for which there exists a continuous real valued function $f: \mathbb{R}\to\mathbb{R}$ such that lip $f$ is finite everywhere and Lip $f$ is infinite exactly on $E$.
In this paper, we give a definition of Eremenko's point of a meromorphic function with infinitely many poles and a condition for its existence in narrow annuli in terms of a covering theorem of annulus.
We show that if $f : \mathbb{A}_{\bar{\mathbb{Q}}}^r \to \mathbb{A}_{\bar{\mathbb{Q}}}^r$ is a regular self-map and $P \in \mathbb{A}^r(\bar{\mathbb{Q}})$ has $\limsup_{n \in \mathbb{N}} \frac{\log{h_{\mathrm{aff}}(f^nP)}}{\log{n}} < 1/r$,…
The joint spectral radius of a bounded set of d times d real or complex matrices is defined to be the maximum exponential rate of growth of products of matrices drawn from that set. A set of matrices is said to satisfy the finiteness…
A major open question in transcendental dynamics asks if it is possible for points in a wandering domain to have bounded orbits, and more strongly, for a wandering domain to iterate only in a bounded domain. In this paper we give a partial…
Suppose that $M$ is a closed, connected, and oriented Riemannian $n$-manifold, $f \colon \mathbb{R}^n \to M$ is a quasiregular map automorphic under a discrete group $\Gamma$ of Euclidean isometries, and $f$ has finite multiplicity in a…
We are concerned with describing the structure of the set of points in the unit interval which, when subjected to rotation by irrational alpha modulo one, for all finite portions of the orbit contain at least as many points in the bottom…
Previously published admissibility conditions for an element of $\{0,1\}^{\mathbb{Z}}$ to be the itinerary of a point of the inverse limit of a tent map are expressed in terms of forward orbits. We give necessary and sufficient conditions…
We analyze the boundaries of multiply connected Fatou components of transcendental maps by means of universal covering maps and associated inner functions. A unified approach is presented, which includes invariant Fatou components (of any…
We show that an entire branched cover of finite distortion cannot have a compact branch set if its distortion satisfies a certain asymptotic growth condition. We furthermore show that this bound is strict by constructing an entire,…
We investigate iterated function systems (IFS) that randomly alternate between two non-identical one-dimensional maps. Our primary focus is on finite invariant sets exhibiting ``toss-and-catch'' dynamics, in which trajectories alternate…
We consider mappings, which are structure consisting of a single function (and possibly some number of unary relations) and address the problem of approximating a continuous mapping by a finite mapping. This problem is the inverse problem…
We give a complete description of the possible Hausdorff dimensions of escaping sets for meromorphic functions with a finite number of singular values. More precisely, for any given $d\in [0,2]$ we show that there exists such a meromorphic…
The possibilities for limit functions on a Fatou component for the iteration of a single polynomial or rational function are well understood and quite restricted. In non-autonomous iteration, where one considers compositions of arbitrary…
We show that, in dimensions $n\geq 3$, continuity and boundedness do not restore the Sobolev regularity conjecture of Iwaniec and Martin for weakly quasiregular mappings below the critical exponent. For every bounded domain…
We study non-autonomous conformal iterated function systems, with finite or countably infinite alphabet alike. These differ from the usual (autonomous) iterated function systems in that the contractions applied at each step in time are…
We study the attractor of Iterated Function Systems composed of infinitely many affine, homogeneous maps. In the special case of second generation IFS, defined herein, we conjecture that the attractor consists of a finite number of…