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Category: Software for maps

The BOV-method: Normally hyperbolic invariant manifolds

The BOV-method is an algorithm for the computation of normally hyperbolic invariant manifolds. The method is based on the graph transform and works in a continuation setting. The BOV-method is not influenced by changes of the dynamics on the manifolds, as long as they are normally hyperbolic.

The BOV-method is implemented for two- three- or four-dimensional diffeomorphisms and computes the following types of manifolds:

• local stable and unstable manifolds of fixed points,
• attracting (or repelling) invariant circles or tori,
• invariant circles or tori of saddle-type,
• local stable and unstable manifolds of invariant circles and tori.

This software cannot be downloaded. However, Hinke Osinga is very interested in applications. Just send her an email and ask!

Contact person for the BOV-method is Hinke Osinga (H.M.Osinga@bristol.ac.uk)

References

• H.W. Broer, H.M. Osinga and G.Vegter
  "Algorithms for computing normally hyperbolic invariant manifolds"
  Z. angew. Math. Phys. 48: 480-524, 1997.
  
  
• H.M. Osinga
  Computing invariant manifolds: An implementation of the graph transform
  Ph.D.-thesis, University of Groningen, 1996.
  
  
• H.W. Broer, H.M. Osinga and G.Vegter
  "On the computation of normally hyperbolic invariant manifolds"
  in H.W. Broer et al. (Eds.) Progress in Nonlinear Differential Equations and Their Applications 19: 423-447, Birkhäuser Verlag, Basel / Switzerland, 1996.
  
  
• H.W. Broer, H.M. Osinga and G.Vegter
  "Computing a normally hyperbolic invariant manifold of saddle type"
  in G.S. Ladde and M. Sambandham (Eds.), Proceedings of Dynamic Systems & Applications 2: 83-90, Dynamic Publishers, Inc., 1996.
  
  
• H.W. Broer, H.M. Osinga and G.Vegter
  "Computing a normally attracting invariant manifold of a Poincaré map"
  in P.L. Butzer, H.Th. Jongen, and W. Oberschelp (Eds.), Charlemagne and His Heritage, 1200 Years of Civilization and Science in Europe, Volume 2: Mathematical Arts, pp. 541-549, Brepols Publishers, 1998.