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This paper proposes an approach to approximate the L YAPUNOV  -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 L YAPUNOV  -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 L YAPUNOV  -spectrum of periodic and quasiperiodic motions of a forced V AN-DER -P OL  equation. The results are compared to results from a classical time integration based method using a continuous G RAM -S CHMIDT  orthonormalization.

Numerical Approximation of LYAPUNOV-Exponents for Quasiperiodic Motions