Related papers: Buried Points in Julia Sets
We consider accumulation of periodic points in local uniformly quasiregular dynamics. Given a local uniformly quasiregular mapping $f$ with a countable and closed set of isolated essential singularities and their accumulation points on a…
In these talks, I discuss a few selected topics in integrable models that are of interest from various points of view. Some open questions are also described.
We provide a formal introduction into the classic theorems of general topology and its axiomatic foundations in set theory. Starting from ZFC, the exposition in this first part includes relation and order theory as well as a construction of…
Special exotic class of dynamical systems~ -- the implicit maps~ -- is considered. Such maps, particularly, can appear as a result of using of implicit and semi-implicit iterative numerical methods. In the present work we propose the…
These are some informal notes concerning topological vector spaces, with a brief overview of background material and basic notions, and emphasis on examples related to classical analysis.
We review a few results concerning interpolation of monotone functions on infinite lattices, emphasizing the role of set-theoretic considerations. We also discuss a few open problems.
We discuss computability and computational complexity of conformal mappings and their boundary extensions. As applications, we review the state of the art regarding computability and complexity of Julia sets, their invariant measures and…
We study the correspondence between unicritical laminations and maximally critical laminations with rotational and identity return polygons. Laminations are a combinatorial and topological way to study Julia sets. Laminations give…
We have studied the concept of bipolarity of information in the soft sets. We have defined bipolar soft sets and basic operations of union, intersection and complementation for bipolar soft sets. Examples of bipolar soft sets and an…
In this manuscript we systematically review known results of local dynamics of discrete local holomorphic dynamics near fixed points in one and several complex variables as well as the consequences in global dynamics.
We introduce one dimensional sets to help describe and constrain the integral curves of an $n$ dimensional dynamical system. These curves provide more information about the system than the zero-dimensional sets (fixed points) do. In fact,…
This article is meant as a mathematical appendix or comment on [BT]. We first consider the notion of transcritical bifurcations of fixed points of general area-preserving maps, and then adress some questions related to [BT] on bifurcation…
We argue that discrete dynamics has natural links to the theory of analytic functions. Most important, bifurcations and chaotic dynamical properties are related to intersections of algebraic varieties. This paves the way to identification…
B. Tanay et. al. introduced and studied fuzzy soft topological spaces. Here we introduce fuzzy soft point and study the concept of neighborhood of a fuzzy soft point in a fuzzy soft topological space. We also study fuzzy soft closure and…
We show that under the definition of computability which is natural from the point of view of applications, there exist non-computable quadratic Julia sets.
Random variables and their distributions are a central part in many areas of statistical methods. The Distributions.jl package provides Julia users and developers tools for working with probability distributions, leveraging Julia features…
In this work we consider a class of endomorphisms of $\mathbb{R}^2$ defined by $f(x,y)=(xy+c,x)$, where $c\in\mathbb{R}$ is a real number and we prove that when $-1<c<0$, the forward filled Julia set of $f$ is the union of stable manifolds…
This is a survey on the local structure about a fixed point of discrete finite-dimensional holomorphic dynamical systems, discussing in particular the existence of local topological conjugacies to normal forms, and the structure of local…
We introduce the concepts of perpetual points and periodic perpetual loci in discrete--time systems (maps). The occurrence and analysis of these points/loci are shown and basic examples are considered. We discuss the potential usage and…
The cluster soft point is an attempt to introduce a novel generalization of the soft closure point and the soft limit point. A cluster soft set is defined to be the system of all cluster soft points of a soft set. Then the fundamental…