A lattice refinement scheme for finding periodic orbits

Authors

  • B.I. Henry
  • S.D. Watt
  • S.L. Wearne

DOI:

https://doi.org/10.21914/anziamj.v42i0.619

Abstract

A lattice refinement scheme based on the principle of linearized stability is introduced to locate periodic orbits in a two-dimensional map. The method locates all periodic orbits of a specified order within a given starting window and it can be equally well applied when the map is only known implicitly, e.g., as a two-dimensional surface of section arising from a three-dimensional flow. Periodic orbits in the Henon Map, the Predator-Prey Map, the Rossler Flow, and the Lorenz Flow are constructed as illustrations of the method.

Published

2000-12-25

Issue

Section

Proceedings Computational Techniques and Applications Conference