The Map of the Courts and the Brazilian Borders

The formation of our borders are analyzed, at first presenting the question of the demarcation line of Tordesillas and the problems that led to the abandonment of this trace to adopt a configuration thatwould deal with both the actual possession of the territory (uti possidetis) as the natural borders formed by rivers and water borders. Next, the Map of the Courts is examined, having served as the basis for the Treaty of Madrid, and it determines, actually, the current configuration of our country. An analysis is made of this cartographic document, with the aid of digital cartography, which yieldeds in the quantity of existing distortions, to modeled its trait and found out how it was built.

Chains of Infinite Order, Chains with Memory of Variable Length, and Maps of the Interval

We show how to construct a topological Markov map of the interval whose invariant probability measure is the stationary law of a given stochastic chain of infinite order. In particular we characterize the maps corresponding to stochastic chains with memory of variable length. The problem treated here is the converse of the classical construction of the Gibbs formalism for Markov expanding maps of the interval.

O mapa das cortes e as fronteiras do Brasil

Analisa-se a formação de nossas fronteiras apresentando inicialmente a questão da demarcação da linha de Tordesilhas e os problemas que levaram ao abandono desse traçado para adotar uma configuração que respeitasse tanto a posse efetiva do território (uti possidetis) como as divisas naturais: rios e divisores de água. A seguir examina-se o Mapa das Cortes que, tendo servido como base para o Tratado de Madri, determinou na prática a configuração atual de nosso país. É feita uma análise desse documento cartográfico, com o auxílio da Cartografia digital, que permitiu quantificar as distorções existentes, afirmar seu caráter propositado e descobrir a forma como foi construído.