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.

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