Related papers: Accesses to infinity from Fatou components
We study a mixed boundary value problem for the quasilinear elliptic equation $\mathop{\rm div}\mathcal{A}(x,\nabla u(x))=0$ in an open infinite circular half-cylinder with prescribed continuous Dirichlet data on a part of the boundary and…
In this work we exploit the notion of N-distal property for a homeomorphisms. We study how it behaves under factor operations. We investigate the relation between N-distality and transitivity, N-equicontinuity and expansivity. We also prove…
We consider the following conjecture (from Huang, et al): Let $\Delta^+$ denote the upper half disc in $\mathbb{C}$ and let $\gamma = ( - 1, 1)$ (viewed as an interval in the real axis in $\mathbb{C}$). Assume that $F$ is a holomorphic…
Multistable coupled map lattices typically support travelling fronts, separating two adjacent stable phases. We show how the existence of an invariant function describing the front profile, allows a reduction of the infinitely-dimensional…
We introduce a natural generalization of Maya diagrams -- the space of infinite Fibonacci configurations, which are specified functions on $\mathbb{Z}$ with values $1$ and $0$. Infinite Fibonacci configurations are particularly interesting…
In this paper we discuss the boundedness of the Fatou components for the sine family and the extended sine family, mainly when the parameter \lambda has modulus greater than 1 and the map is post-critically bounded.
We study the class $\mathcal{M}$ of functions meromorphic outside a countable closed set of essential singularities. We show that if a function in $\mathcal{M}$, with at least one essential singularity, permutes with a non-constant rational…
In this paper, we settle a long-standing problem on the connectivity of spaces of finite unit norm tight frames (FUNTFs), essentially affirming a conjecture first appearing in [Dykema and Strawn, 2003]. Our central technique involves…
We show a partial generalization of Sullivan's non-wandering domain theorem in complex dimension two. More precisely, we show the non-existence of wandering Fatou components for polynomial skew products of $ \mathbb{C}^2$ with an invariant…
We study the continuity of half-plane capacity as a function of boundary hulls with respect to the Carath\'eodory convergence. In particular, our interest lies in the case that hulls are unbounded. Under the assumption that every hull is…
We present recent advances in harmonic analysis on infinite graphs. Our approach combines combinatorial tools with new results from the theory of unbounded Hermitian operators in Hilbert space, geometry, boundary constructions, and spectral…
In this paper, we study the Martin kernels of general open sets associated with inaccessible points for a large class of purely discontinuous Feller processes in metric measure spaces. Let $D$ be an unbounded open set. Infinity is…
We use the complexity function of an invariant, not necessary closed, subset of a two-sided shift space to compute the polynomial entropy of the induced dynamics on the hyperspace of continua for certain one-dimensional dynamical systems.…
We study two-dimensional conformal field theories (CFTs) with boundaries via the conformal bootstrap. We derive a positive semi-definite program from crossing symmetry of three observables: the annulus partition function, the two-point…
We first establish any continuum without interiors can be a limit set of iterations of an entire function on an oscillating wandering domain, and hence arise as a component of Julia sets. Recently, Luka Boc Thaler showed that every bounded…
Given a parameter dependent fixed point equation $x = F(x,u)$, we derive an abstract compactness principle for the fixed point map $u \mapsto x^*(u)$ under the assumptions that (i) the fixed point equation can be solved by the contraction…
We consider polynomial maps of the form f(z,w) = (p(z),q(z,w)) that extend as holomorphic maps of CP^2. Mattias Jonsson introduces in (Math. Ann., 1999) a notion of connectedness for such polynomial skew products that is analogous to…
We study the dynamics near infinity of polynomial mappings $f$ in $\mathbb{C}^2$. We assume that $f$ has indeterminacy points and is non constant on the line at infinity $L_\infty$. If $L_\infty$ is $f$-attracting, we decompose the Green…
Let $\rho_0$ be an action of a Lie group on a manifold with boundary that is transitive on the interior. We study the set of actions that are topologically conjugate to $\rho_0$, up to smooth or analytic change of coordinates. We show that…
Consider a Hausdorff space (X,T) and a set C of converging nets in X. By virtue of the limit uniqueness, the relation Lim which assigns each member x of X to every net N lying in C that converges to x is a map. Of course, structuring C with…