Stretching rates in discrete dynamical systems (Q1573919)

The asymptotic behaviour of trajectories in nonlinear dynamical systems in \(\mathbb{R}^n\) (for \(t\to\infty)\) can be characterized by stretching and/or shrinking rates of volume elements in different directions. Fixed points, cycles, tori and chaotic attractors are different types of attractors, which are distinguishable by their Lyapunov exponents connected with these stretching rates. The author shows that the singular value decomposition of the Jacobian matrix is a useful technique for calculating the maximal stretching rates and the corresponding maximal Lyapunov exponents.