Related papers: Topological conjugation of one dimensional maps
We prove that two topologically conjugate bi-critical circle maps whose signatures are the same, and whose renormalizations converge together exponentially fast in the $C^2$-topology, are $C^1$ conjugate.
Different cell types aggregate and sort into hierarchical architectures during the formation of animal tissues. The resulting spatial organization depends (in part) on the strength of adhesion of one cell type to itself relative to other…
We introduce a new technique to study pattern avoidance in dynamical systems, namely the use of a commuter function between non-conjugate dynamical systems. We investigate the properties of such a commuter function, specifically $h : [0,1]…
Each graph and choice of a commutative ring gives rise to an associated graphical group. In this article, we introduce and investigate graph polynomials that enumerate conjugacy classes of graphical groups over finite fields according to…
Many works have studied the Internet topology, but few have investigated the question of how it evolves over time. This paper focuses on the Internet routing IP-level topology and proposes a first step towards realistic modeling of its…
A general scheme is proposed and tested to control the symmetry breaking instability of a homogeneous solution of a spatially extended multispecies model, defined on a network. The inherent discreteness of the space makes it possible to act…
Using the idea of the degree of a smooth mapping between two manifolds of the same dimension we present here the topological (homotopical) classification of the mappings between spheres of the same dimension, vector fields, monopole and…
In this paper we study the one dimensional random geometric graph when the location of the nodes are independent and exponentially distributed. We derive exact results and the limit theorems for the connectivity and other properties…
Alignment interactions in active matter are typically modeled as relaxational dynamics toward local consensus. In unbounded systems, this makes alignment effectively decoupled from local density and therefore unable to sustain self-confined…
We establish necessary and sufficient conditions for a dynamical system to be topologically conjugate to the Morse minimal set, the shift orbit closure of the Morse sequence, and conditions for topological conjugacy to the closely related…
The article is devoted to a structure of topological spaces related with topological quasigroups. Regular and complete spaces over topological quasigroups are studied. Separations and embeddings are also investigated for them. Their…
We study the neutral periodic points of the Markov-Dyck shifts of finite strongly connected directed graphs. Under certain hypothesis on the structure of the graphs we show, that the topological conjugacy of their Markov-Dyck shifts implies…
We study synchronization of non-diffusively coupled map networks with arbitrary network topologies, where the connections between different units are, in general, not symmetric and can carry both positive and negative weights. We show that,…
Two-dimensional mappings obtained by coupling two piecewise increasing expanding maps are considered. Their dynamics is described when the coupling parameter increases in the expanding domain. By introducing a coding and by analysing an…
In this paper, we focus on some properties, calculations and estimations of topological entropy for a nonautonomous dynamical system $(X,f_{0,\infty})$ generated by a sequence of continuous self-maps $f_{0,\infty}=\{f_n\}_{n=0}^{\infty}$ on…
Arguments inspired by algorithmic information theory predict an inverse relation between the probability and complexity of output patterns in a wide range of input-output maps. This phenomenon is known as \emph{simplicity bias}. By viewing…
This is a significantly expanded version of the survey paper "Mixing and decay of correlations in non-uniformly expanding maps: a survey of recent results" math/0301319. We discuss recent results on decay of correlations for non-uniformly…
In this work we introduce a topological method for the search of fixed points and periodic points for continuous maps defined on generalized rectangles in finite dimensional Euclidean spaces. We name our technique "Stretching Along the…
This is a chapter in an incoming book on aperiodic order. We review results about the topology, the dynamics, and the combinatorics of aperiodically ordered tilings obtained with the tools of noncommutative geometry.
We continue our study of the dynamics of mappings with small topological degree on (projective) complex surfaces. Previously, under mild hypotheses, we have constructed an ergodic ``equilibrium'' measure for each such mapping. Here we study…