Fractal dimensions of hyperbolic graphs and horseshoes

• Autor(a) principal: Deberton Moura de Oliveira
• Data de Publicação: 2022
• Tipo de documento: Dissertação
• Idioma: eng
• Título da fonte: Repositório Institucional da UFMG
• Texto Completo: http://hdl.handle.net/1843/46723
• topic: Fractal Geometry; Hausdorff Dimension; Box Dimension; Hyperbolic Graphs; Horseshoe; Geometria Fractal; Dimensão Hausdorff; Dimensão Caixa; Conjuntos Hiperbólicos; Ferradura; Matemática – Teses; Geometria – Teses; Fractais – Teses; Grupos hiperbólicos – Teses

Fractal Geometry is a field of Mathematics under development, which is open for expansion and new insights. Moreover, fractals are objects that arouses curiosity, since these objects have unorthodox properties, an irregular geometry and some self-similarities. On the other hand, since it is an area in development, there are some distinct fractal dimension calculations for hyperbolic graphs, as we are going to present here, based on two articles. The first paper calculates the Hausdorff dimension of a horseshoe using its intersection with the unstable manifold, with a strong usage of ergodic theory and hyperbolic dynamics. However, the second paper calculates the box dimension of an attractor by almost periodic functions and Fourier series, with a bit of hyperbolic dynamics.