Computing Invariant Tori and Circles in Dynamical Systems

@inproceedings{Reichelt2004ComputingIT,
  title={Computing Invariant Tori and Circles in Dynamical Systems},
  author={Volker Reichelt},
  year={2004}
}
We present several algorithms to compute invariant tori in a family of dynamical systems using a continuation strategy. The algorithms are based on the discretization of the graph transform. To circumvent two problems of the standard approach (which requires solving ordinary BVPs) we modify the discretized graph transform. This results in faster and more robust methods. 
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Referenced Papers

Publications referenced by this paper.
Showing 1-10 of 11 references

AUTO94: Software for continuation and bifurcation problems in ordinary differential equations, Technical report, CRPC-95-2, Center for Research on Parallel Computing, California Institute

  • E. J. Doedel, X. J. Wang
  • 1995
Highly Influential
4 Excerpts

Othmer, An analytical and numerical study of the bifurcations in a system of linearly-coupled oscillators

  • D. G. Aronson, H.G.E.J. Doedel
  • Physica D,
  • 1987
Highly Influential
4 Excerpts

Computation of invariant tori by the method of characteristics

  • L. Dieci, J. Lorenz
  • SIAM J. Numer. Anal.,
  • 1995
Highly Influential
4 Excerpts

Persistence and Smoothness of Invariant Manifolds for Flows

  • N. Fenichel
  • Indiana University Mathematics Journal,
  • 1971
Highly Influential
3 Excerpts

Algorithms for computing normally hyperbolic invariant manifolds

  • H. M. Osinga H. W. Broer, G. Vegter
  • Z . Angew . Math . Phys .
  • 1997

Algorithms for computing normally hyperbolic invariant manifolds, Z

  • H. W. Broer, H. M. Osinga, G. Vegter
  • Angew. Math. Phys.,
  • 1997
2 Excerpts

Computation and parametrisation of invariant curves and tori

  • G. Moore
  • SIAM J. Numer. Anal.,
  • 1996
3 Excerpts

An analytical and numerical study of the bifurcations in a system of linearlycoupled oscillators

  • E. J. Doedel, H. G. Othmer
  • 1987

Nonlinear oscillations, dynamical systems, and bifurcations of vector fields, Springer Series in Applied

  • J. Guckenheimer, Ph. Holmes
  • Mathematical Sciences
  • 1983

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