Numerical Solutions and Parameter Sensitivity of the Lorenz System

Abstract: In chaos theory there are many different problems still unsolved. One of which is the optimization of infinite time average functionals on manifolds. To try one of the different tools to solve this problem we want to find stable manifolds in chaotic dynamical systems.In this thesis we find different manifolds for the Lorenz system when using a time dependent $\mu$ parameter and perform a sensitivity analysis on some of them. The existence of these manifolds are motivated numerically with the help of the shadowing lemma and extensive comparison of different numerical solvers.