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Category: Software for maps

Two-dimensional global unstable manifolds of maps

In contrast to the computation of one-dimensional stable and unstable manifolds, little is known about globalizing higher dimensional manifolds. With the software of Bernd Krauskopf and Hinke Osinga, it is possible to compute two-dimensional manifolds of either a hyperbolic fixed point or a normally hyperbolic invariant circle.

The development of software for globalizing two-dimensional manifolds is an ongoing project.

This software cannot be downloaded. However, Bernd Krauskopf and Hinke Osinga are very interested in applications of their software. Just send them an email and ask!

Contact persons for Global Manifolds are:
Bernd Krauskopf (B.Krauskopf@bristol.ac.uk) and
Hinke Osinga (H.M.Osinga@bristol.ac.uk)

References

• B. Krauskopf & H.M. Osinga (1998)
  Globalizing two-dimensional unstable manifolds of maps
  Int. J. Bifurcation & Chaos 8(3): 483-503 (abstract or PDF source (1.515Mb) or animations).
  
  
• B. Krauskopf and H.M. Osinga (1998)
  Growing 1D and quasi 2D unstable manifolds of maps (abstract)
  J. Comput. Phys. 146(1): 404-419.