In chapter 1, we are concerned with the explanation of the exponential and Guassian distributions from a geometrical point of view. It is explained how these equilibrium distributions are reached just with the equipartition hypothesis in open and closed statistical systems.
In chapter 2, two nonlinear evolution operators (models) in the space of distributions are built. It is found that the final equilibrium states (fixed points) for these operators are just the exponencial and the Gaussian distributions.
In chapter 3, some simulations of the operators introduced in Ch. 2 are shown for different initial distributions in both models.
(This Graduation Thesis was defended by Iván Allué on July 12, 2017, at the Faculty of Science, Univ. of Zaragoza, Spain).