Numerical continuation of closed invariant curves of maps and its implementation in the MATLAB software MatContM

Abstract

This Bachelor Thesis aims at developing new methods for continuation of closed invariant curves of multi-dimensional diffeomorphisms and their actual implementation in MatContM. This soft-ware includes the standard predictor-corrector code to continue 1D solution branches implicitly defined by systems of algebraic equations. Thus, the main task is to formulate and implementa new defining system to continue closed invariant curves with constant rotation number in two control parameters. These defining equations are based on the Fourier approximation of the closed invariant curve and the discretization of the invariancy condition. An auxiliary but important subtask is to implement an initialization algorithm to start continuation of closed invariant curves from a given point in the Neimark-Sacker bifurcation curve.