Restrict three body problem

Author(s)

Fernando Pereira Micena

• Document type: Master's Dissertation
• Press: São Carlos.
• Institution: Universidade de São Paulo (USP). Instituto de Ciências Matemáticas e de Computação (ICMC/SB)
• Defense date: 2007-02-23

Examining board members

Ali Tahzibi; Carlos Alberto Maquera Apaza; Claudio Aguinaldo Buzzi

• Advisor: Ali Tahzibi

Abstract

The n?body problem is one of the most important problems in dynamical systems. We study the model introduced by Sitnikov of restricted three body problem. In this model the primaries are of equal mass and the third body is very small with respect to the primaries. Using methods of Alekseev, we show the existence of ?Smale horseshoe?as a subsystem of the dynamic of the third body and conclude rich probabilistic consequences. We also study the same problem by Melnikov?s method (AU)