Related papers: Unbounded fast escaping wandering domains

We study the evolution of a random walker on a conservative dynamic random environment composed of independent particles performing simple symmetric random walks, generalizing results of [16] to higher dimensions and more general transition…

We consider the dynamics associated with an arbitrary semigroup of transcendental entire functions. Fatou-Julia theory is used to investigate the dynamics of these semigroups. Several results of the dynamics associated with iteration of a…

Complex or hostile environments can sometimes inhibit the movement capabilities of diffusive particles or active swimmers, who may thus become stuck in fixed positions. This occurs, for example, in the adhesion of bacteria to surfaces at…

We aim to describe a droplet bouncing on a vibrating bath using a simple and highly versatile model inspired from quantum mechanics. Close to the Faraday instability, a long-lived surface wave is created at each bounce, which serves as a…

For an infinite class of finite graphs of unbounded size, we define a limit object, to be called a $\textit{wide limit}$, relative to some computationally restricted class of functions. The limit object is a first order Boolean-valued…

A simple and very accurate method to approximate a function with a finite number of discontinuities is presented. This method relies on hyperbolic tangent functions of rational arguments as connecting functions at the discontinuities, each…

We derive explicit upper bounds for the $\bar{d}$-distance between a chain of infinite order and its canonical $k$-steps Markov approximation. Our proof is entirely constructive and involves a "coupling from the past" argument. The new…

Let K be a non-archimedean field with residue field k, and suppose that k is not an algebraic extension of a finite field. We prove two results concerning wandering domains of rational functions f in K(z) and Rivera-Letelier's notion of…

Transcendental functions, such as exponentials and logarithms, appear in a broad array of computational domains: from simulations in curvilinear coordinates, to interpolation, to machine learning. Unfortunately they are typically expensive…

In this article, we present explicit estimates of the size of the domain on which the Implicit Function Theorem and the Inverse Function Theorem are valid. For maps that are twice continuously differentiable, these estimates depend upon the…

Large optimal transport problems can be approached via domain decomposition, i.e. by iteratively solving small partial problems independently and in parallel. Convergence to the global minimizers under suitable assumptions has been shown in…

We study, in d-dimensions, the random walker with geometrically shrinking step sizes at each hop. We emphasize the integrated quantities such as expectation values, cumulants and moments rather than a direct study of the probability…

We prove two separate lower bounds -- one for nondegenerate convex domains and the other for nondegenerate $\mathbb{C}$-convex (but not necessarily convex) domains -- for the squeezing function that hold true for all domains in…

We introduce and study a dimensional-like characteristic of an uniformly almost periodic function, which we call the Diophantine dimension. By definition, it is the exponent in the asymptotic behavior of the inclusio length. Diophantine…

Let $f$ be a transcendental entire function of finite order which has an attracting periodic point $z_0$ of period at least $2$. Suppose that the set of singularities of the inverse of $f$ is finite and contained in the component $U$ of the…

Let $f$ be a transcendental entire function. The quite fast escaping set, $Q(f)$, and the set $Q_2(f),$ which was defined recently, are equal to the fast escaping set, $A(f),$ under certain conditions. In this paper we generalise these sets…

In this paper, we prove the existence of nontrivial unbounded domains $\Omega\subset\mathbb{R}^{n+1},n\geq1$, bifurcating from the straight cylinder $B\times\mathbb{R}$ (where $B$ is the unit ball of $\mathbb{R}^n$), such that the…

We study the regularity of the distance function to the boundary of a domain in $\mathbb{R}^n$, with respect to the Minkowski functional of a convex polytope. We obtain the regularity of the distance function in certain cases. We also…

We prove that for every indecomposable ordinal there exists a (transfinitely valued) Euclidean domain whose minimal Euclidean norm is of that order type. Conversely, any such norm must have indecomposable type, and so we completely…

The problem of reconstructing functions from their asymptotic expansions in powers of a small variable is addressed by deriving a novel type of approximants. The derivation is based on the self-similar approximation theory, which presents…