Numerical Approximation of LYAPUNOV-Exponents for Quasiperiodic Motions

Abstract

This paper proposes an approach to approximate the LYAPUNOV -spectrum of quasiperiodic flows on isolated invariant manifolds numerically. Once the invariant manifold has been determined, integrations over the infinite, one dimensional time interval – as calculating the LYAPUNOV -spectrum for instance – can be transformed into an integral over a finite, p-dimensional domain, where p is the dimension of the manifold. The application of the proposed approach is demonstrated by calculating the LYAPUNOV -spectrum of periodic and quasiperiodic motions of a forced VAN-DER-POL equation. The results are compared to results from a classical time integration based method using a continuous GRAM-SCHMIDT orthonormalization.