Rugosidade em bilhares clássicos

Abstract

In this work we are going to study a physical system known as billiard. A billiard is defined to be basically a confined particle in a closed region of the space. We are going to deal with only two-dimensionals billiards in the absence of extern fields and to neglect any kind of dissipative forces, in a way that the colisions of the particle with the boundary are elastics. Beyond that, the boundary are fixed, it means they respect an equation of kind R(r, 9), where r and O are the polar coordinates on a plan. A billiard is a very interesting model by several reasons. First, it is a simple system (it has a few degree of freedom) and it is of easy visualization. However, it has a non-trivial dynamics with a big richness of behaviors (from a billiard it could appear regular behavior, chaotic behavior, or even a mixed behavior, where coexist in the phase space of one billiard chaotics and regular regions). Second, the numerical approach of these systems does not require numerical integration of diferential equations and, therefore, does not take too much time of execution. Furthermore, the billiards allow us to perform investigations of fundamental nature, for example, we can study how regular systems react by being slightly disturbed. Especificaly, we perform a rugosity perturbation on the billiard surface and observe how the phase space is going to change.