Summary.
We consider a dissipative perturbation of non–resonant harmonic oscillators. Under the perturbation the system admits a weakly attractive invariant torus. We apply a Runge-Kutta method to the system. If the integration method is symplectic then it also admits an attractive invariant torus, the step-size being independent of the perturbation parameter. For non–symplectic methods the discrete system only admits an attractive invariant torus if the step-size is so small such that the discretisation error is smaller than the perturbation.
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Received May 17, 1996
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Stoffer, D. On the qualitative behaviour of symplectic integrators Part I: Perturbed linear systems. Numer. Math. 77, 535–547 (1997). https://doi.org/10.1007/s002110050299
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DOI: https://doi.org/10.1007/s002110050299