On discrete models of fractal dimension to explore the complexity of discrete dynamical systems

Área de investigación: Applied Mathematics Año: 2017
Tipo de publicación: Artículo Palabras clave: Discrete dynamical system; fractal structure; fractal dimension; box-counting dimension; chaos measure
Autores: Fernández Martínez, Manuel; Rodríguez-Bermúdez, Germán; Vera, J. A.
Journal: Journal of Difference Equations and Applications Volumen: 23
Número: 1-2 Páginas: 258-274
Mes: August
ISSN: 1023-6198
A fractal structure is a countable family of coverings which displays accurate information about the irregularities that a set presents when being explored with enough level of detail. It is worth noting that fractal structures become especially appropriate to provide new definitions of fractal dimension, which constitutes a valuable measure to test for chaos in dynamical systems. In this paper, we explore several approaches to calculate the fractal dimension of a subset with respect to a fractal structure. These models generalize the classical box dimension in the context of Euclidean subspaces from a discrete viewpoint. To illustrate the flexibility of the new models, we calculate the fractal dimension of a family of self-affine sets associated with certain discrete dynamical systems.
Texto completo: paper pedro.pdf