相关论文: Spiders' webs in the punctured plane

Using computer graphics and visualization algorithms, we extend in this work the results obtained analytically in [1], on the connectivity domains of alternated Julia sets, defined by switching the dynamics of two quadratic Julia sets. As…

Many real-world complex systems such as social, biological, information as well as technological systems results of a decentralized and unplanned evolution which leads to a common structuration. Irrespective of their origin, these so-called…

Food webs -- networks of predators and prey -- have long been known to exhibit "intervality": species can generally be ordered along a single axis in such a way that the prey of any given predator tend to lie on unbroken compact intervals.…

We prove that every transcendental meromorphic map f with a disconnected Julia set has a weakly repelling fixed point. This implies that the Julia set of Newton's method for finding zeroes of an entire map is connected. Moreover, extending…

Let $f$ be a transcendental entire function. The escaping set $I(f)$ consists of those points that tend to infinity under iteration of $f$. We show that $I(f)$ is not $\sigma$-compact, resolving a question of Rippon from 2009.

The understanding of the immense and intricate topological structure of the World Wide Web (WWW) is a major scientific and technological challenge. This has been tackled recently by characterizing the properties of its representative graphs…

We study the dynamics of an arbitrary semigroup of transcendental entire functions using Fatou-Julia theory. Several results of the dynamics associated with iteration of a transcendental entire function have been extended to transcendental…

A spanning generalized caterpillar is a spanning tree in which all vertices of degree more than two are on a path. In this note, we find a relation between the existence of spanning generalized caterpillar and the independence and…

We describe the spreading property for finite transitive permutation groups in terms of properties of their associated coherent configurations, in much the same way that separating and synchronising groups can be described via properties of…

Let $f$ be a transcendental entire function and $U$ be a Fatou component of $f$. We show that if $U$ is an escaping wandering domain of $f$, then most boundary points of $U$ (in the sense of harmonic measure) are also escaping. In the other…

We study the topology of the Megaparsec Cosmic Web on the basis of the Alpha Shapes of the galaxy distribution. The simplicial complexes of the alpha shapes are used to determine the set of Betti numbers ($\beta_{\rm k},k=1,...,D$), which…

Spiders are arthropods that can be distinguished from their closest relatives, the insects, by counting their legs. Spiders have 8, insects just 6. Spider graphs are a very restricted class of graphs that naturally appear in the context of…

We work with combinatorial maps to represent graph embeddings into surfaces up to isotopy. The surface in which the graph is embedded is left implicit in this approach. The constructions herein are proof-relevant and stated with a subset of…

The topological structures of the Internet and the Web have received considerable attention. However, there has been little research on the topological properties of individual web sites. In this paper, we consider whether web sites (as…

Mutualistic networks have been shown to involve complex patterns of interactions among animal and plant species. The architecture of these webs seems to pervade some of their robust and fragile behaviour. Recent work indicates that there is…

Given two permutable entire functions $f$ and $g,$ we establish vital relationship between escaping sets of entire functions $f, g$ and their composition. We provide some families of transcendental entire functions for which Eremenko's…

A method to compute the full hierarchy of the critical subsets of a density field is presented. It is based on a watershed technique and uses a probability propagation scheme to improve the quality of the segmentation by circumventing the…

Despite its increasing role in communication, the world wide web remains the least controlled medium: any individual or institution can create websites with unrestricted number of documents and links. While great efforts are made to map and…

We study asymptotic dynamics in networks of coupled quadratic nodes. While single map complex quadratic iterations have been studied over the past century, considering ensembles of such functions, organized as coupled nodes in a network,…

A generalized family of transcendental (non-polynomial entire) functions is constructed, where the Hausdorff dimension and the packing dimension of the Julia sets are equal to one. Further, there exist multiply connected wandering domains,…