Reconstructing noisy dynamical systems by triangulations

We show how to construct triangulations of noisy data from dynamical systems. We model the dynamics using piecewise linear or C-1 models defined over the triangulation. The number and positions of vertices of the triangulation are selected by the minimum description length criterion. We test the method on two artificial data sets and on experimental data from a chaotic electronic circuit. The models reproduce the qualitative aspects of the data as well as quantitative aspects such as correlation dimension and periodic points.