A Note on the periodic orbits and topological entropy of graph maps

This paper deals with the relationship between the periodic orbits of continuous maps on graphs and the topological entropy of the map. We show that the topological entropy of a graph map can be approximated by the entropy of its periodic orbits

The normal distribution in some constrained sample spaces

Phenomena with a constrained sample space appear frequently in practice. This is the case e.g. with strictly positive data, or with compositional data, like percentages or proportions. If the natural measure of difference is not the absolute one, simple algebraic properties show that it is more convenient to work with a geometry different from the usual Euclidean geometry in real space, and with a measure different from the usual Lebesgue measure, leading to alternative models which better fit the phenomenon under study. The general approach is presented and illustrated using the normal distribution, both on the positive real line and on the D-part simplex. The original ideas of McAlister in his introduction to the lognormal distribution in 1879, are recovered and updated

Otra mirada al tema del cambio de escala: los nuevos espacios de comercio, ocio y turismo = Another look at the theme of the change of scale: new spaces in commerce, leisure and tourism

The technological advances and new organisation of the economy together with a change in ideas in consumer habits andlifestyle that have happened in the last 25 years have placed us in a new state of capitalism. The spatial translation of thisnew state has been immediate and implies among other changes the overcoming of the concept of scale. Commercialspaces and those of leisure and tourism offer us an unbeatable opportunity of exemplifying these changes because they arethe most effected by the new postmodern tendencies

Espacios olvidados, lugares diferenciados: transformación social del espacio urbano en Bogotá (1850- 1880) = Forgotten Spaces, distinct places: Social transformation of urban space in Bogotá (1850-1880)

The purpose of this article is linked to some forms of recovery of social and urban spaces fallen into oblivion that are evident in the social transformation of urban space in Bogotá between 1850 and 1880.The following paper presents the preliminary results of the research entitled practices and social uses of water in Bogotá (1850-1888). The text links in first discussions about the understanding of the city as a drawing in space, moving to describe, the growth of the city, integrating its historical, social and cultural structuring