@article{dfbbabc0b53f4556a51daf864a5be3ab,
title = "Continuation of quasi-periodic invariant tori",
abstract = "Many systems in science and engineering can be modeled as coupled or forced nonlinear oscillators, which may possess quasi- periodic or phase- locked invariant tori. Since there exist routes to chaos involving the break- down of invariant tori, these phenomena attract considerable attention. This paper presents a new algorithm for the computation and continuation of quasi- periodic invariant tori of ODEs that is based on a natural parametrization of such tori. Since this parametrization is uniquely defined, the proposed method requires neither the computation of a base of a transversal bundle nor remeshing during continuation. It is independent of the stability type of the torus, and examples of attracting and saddle- type tori are given. The algorithm is robust in the sense that it can compute approximations to weakly resonant tori. The performance of the method is demonstrated with examples.",
author = "F Schilder and HM Osinga and W Vogt",
note = "Publisher: Society for Industrial and Applied Mathematics",
year = "2005",
month = jan,
doi = "10.1137/040611240",
language = "English",
volume = "4 (3)",
pages = "459 -- 488",
journal = "SIAM Journal on Applied Dynamical Systems",
issn = "1536-0040",
publisher = "Society of Industrial and Applied Mathematics",
}