Relações entre análise, sistemas dinâmicos e geometria fractal com teoria dos números

Abstract

This work aims to show some applications of Analysis, Fractal Geometry and Dynamic systems in Number Theory. In the first part we present arithmetic functions and prove some results, evolving to the study of Dirichlet characters to prove Pólya’s Inequality and Dirichlet’s Theorem for primes in arithmetic progressions. In the second part we study sets called fractals, calculating their dimensions and discovering their properties and derived characteristics. The techniques developed and the knowledge acquired allow us to prove results in continued fractions and Jarnik’s Theorem, in the area of diophantine approximations.