On elastic graph spines associated to quadratic Thurston maps

Exponential Thurston Maps and Limits of Quadratic Differentials

Contents 1. Introduction 2 Organization of the paper 3 2. The characterization theorem 4 2.1. Definitions and statement of the main theorem 4 2.2. Classification of postsingularly finite exponential maps 4 3. Iteration in Teichmüler space 6 3.1. The Teichmüler space of a topological exponential map 7 3.2. The Teichmüler metric and its dual 8 3.3. Examples of quadratic differentials 9 3.4. Proof...

On Nearly Euclidean Thurston Maps

Nearly Euclidean Thurston Maps

We take an in-depth look at Thurston’s combinatorial characterization of rational functions for a particular class of maps we call nearly Euclidean Thurston maps. These are orientation-preserving branched maps f : S2 → S2 whose local degree at every critical point is 2 and which have exactly four postcritical points. These maps are simple enough to be tractable, but are complicated enough to ha...

A Note on a graph associated to a commutative ring

The rings considered in this article are commutative with identity. This article is motivated by the work on comaximal graphs of rings.  In this article, with any ring $R$, we associate an undirected graph denoted by $G(R)$, whose vertex set is the set of all elements of $R$ and distinct vertices $x,y$ are joined by an edge in $G(R)$ if and only if $Rxcap Ry = Rxy$.  In Section 2 of this articl...

A Note on Quadratic Maps for Hilbert Space Operators

In this paper, we introduce the notion of sesquilinear map on Β(H) . Based on this notion, we define the quadratic map, which is the generalization of positive linear map. With the help of this concept, we prove several well-known equality and inequality...