Orbitas periodicas e suas bifurcações em bilhares magneticos
AUTOR(ES)
Luis Gregorio G. de V. Dias da Silva
DATA DE PUBLICAÇÃO
1997
RESUMO
In this work we have made a detailed study on the search for periodic orbits on two types of Billiards with a ortoghonal magnetic field applied: the Square Billiard and Sinai s Billiard. We have implemented an efficient method of searching directly on Birkhoff s Section Map, which is based on a process of successive iterations, starting from a "test-orbit" and getting the convergence to an "effectively periodic" orbit, having as a convergence parameter the Monodromy Matrix of the orbit. We have obtained about 2000 orbits for both systems, which have been catalogued by stability, action and period. We have made a statistical analysis centered on the number of orbits as a function of several parameters. It was detected a near exponential growth as a function of period and action. For low values of the Magnetic Field, the number of orbits with 2n bounces grows more rapidly than the number of orbits with 2n+l bounces on the Square Billiard. It was observed the presence of "trapping" orbits on Sinai s Billiard for intermediary Magnetic Fields
ASSUNTO(S)
teoria da bifurcação caos metodo de orbitas
