Aproximació de corbes invariants de difeomorfismes

Abstract

This bachelor’s degree final thesis deals with what happens in the neighborhood of a equilibrium point of a differential equation which was added a periodic perturbation or a quasiperiodic perturbation. A first approximation, we will consider the case with a periodic map. After that, we will study the case with a quasiperiodic map. In both cases, the idea is to use a Poincar ́e’s map to find invariant manifolds around the equilibrium point of the initial differential equation. For doing it, we need new concepts that have not been seen throughout the bachelor as differential calculus in Banach spaces. Other results, however, are extension Theorems already seen throughout the bachelor but for Banach spaces, as the Stone-Weierstrass’Theorem. Finally, we have performed a library in C programming language that is optimized pursuing shared memory parallelism in certain parts of its code. In this part, we have applied concepts and results that have been learned in some subjects as operating systems or numerical methods. Some examples and results have been generated using the library and programs to display scientific data.