WIAS Preprint No. 327, (1997)

Periodic solutions of autonomous systems under discretization


  • Bobylev, Nikolai A.
  • Kloeden, Peter E.

2010 Mathematics Subject Classification

  • 47H11 47H30


  • autonomous ordinary differential equation, periodic solution, non-zero topological index, Hausdorff metric




The existence of a sequence of periodic trajectories of a general one-step numerical scheme corresponding to a null sequence of constant time-steps is established under the assumption that the autonomous ordinary differential equation has an isolated periodic solution with non-zero topological index. The convergence of the linearly interpolated numerical curve to the original invariant curve with respect to the Hausdorff metric is also shown.

Appeared in

  • Numer. Funct. Anal. Optim., 18 (1997), no. 7 & 8, pp. 659-665

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