相关论文: On Latt\`es Maps
This chapter is an introduction to the connection between random matrices and maps, i.e graphs drawn on surfaces. We concentrate on the one-matrix model and explain how it encodes and allows to solve a map enumeration problem.
The paper contains an interesting generalization of the classical Taylor expansion formula and four applications
We introduce {\it twist unimodal maps} of the interval and describe their structure. Sufficient conditions for the growth of over-rotation interval in families of maps are given.
Some fixed point results are given for a class of Meir-Keeler contractive maps acting on metric spaces endowed with locally transitive relations. Technical connections with the related statements due to Berzig et al [Abstr. Appl. Anal.,…
This chapter deepens cartographic communication through a cartographic multirepresentation exercise. Using a single dataset on World population data, the chapter presents a series of 13 different maps to illustrate how mapping is primarily…
In this text, we wish to provide the reader with a short guide to recent works on the theory of dilatations in Commutative Algebra and Algebraic Geometry. These works fall naturally into two categories: one emphasises foundational and…
This document contains a description of several of my papers, including remarks on history and connection with subsequent work. It also contains some new results and conjectures.
Further extensions are given to the fixed point result (for implicit contractions) due to Altun and Simsek [Fixed Point Th. Appl., Volume 2010, Article ID 621469]. Some connections with related statements in the area due to Agarwal,…
We introduce the Leavitt path algebras of ultragraphs and we characterize their ideal structures. We then use this notion to introduce and study the algebraic analogous of Exel-Laca algebras.
We prove that a Latt' es map admits an eventually simply-connected wandering continuum precisely when it is flexible. The simply-connected wandering continuum is a line segment in a bi-infinite geodesic under the flat metric.
For any row-finite graph $E$ and any field $K$ we construct the {\its Leavitt path algebra} $L(E)$ having coefficients in $K$. When $K$ is the field of complex numbers, then $L(E)$ is the algebraic analog of the Cuntz Krieger algebra…
We introduce the \emph{Collatz conjecture} and its history. Some definition that this conjecture has, will be expressed and with these we try to explain some good lemma to justify the main properties of the \emph{Collatz conjecture}. With…
This article presents how ship trajectories have been built from historical sources dealing with maritime trade in the 18th century. It first summarizes the method for building the routes, and qualifying the uncertainty level linked to each…
The classical Gauss Map is a piecewise continuous map from the unit interval to itself. From this map we retrieve the continued fraction expansion of irrational numbers and its dynamical properties give information about some arithmetic and…
A short proof of a theorem of M.H. Albert, and its application to lattices.
The iteration of rational maps is well-understood in dimension 1 but less so in higher dimensions. We study some maps on spaces of matrices which present a weak complexity with respect to the ring structure. First we give some properties of…
Lattice results in supersymmetry are summarized. Past, present and future perspectives are discussed.
This is a revised version of the preprint which has been available electronically for a while. The paper will now appear in J. Ramanujan Math. Soc.
It is shown that for a certain class of Yang-Baxter maps (or set-theoretical solutions to the quantum Yang-Baxter equation) the Lax representation can be derived straight from the map itself. A similar phenomenon for 3D consistent equations…
This work studies certain aspects of graphs embedded on surfaces. Initially, a colored graph model for a map of a graph on a surface is developed. Then, a concept analogous to (and extending) planar graph is introduced in the same spirit as…