@techreport{6b656ddbb8c549d9bfc2413d6cb82fca,
title = "Continuation of quasi-periodic invariant tori",
abstract = "Many systems in science and engineering can be modelled 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 ordinary differential equations that is based on a natural parametrisation of such tori. Since this parametrisation is uniquely defined, the proposed method requires neither the computation of a base of a transversal bundle, nor re-meshing 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.",
keywords = "finite-difference method, invariant tori, invariance condition, continuation",
author = "F Schilder and HM Osinga and W Vogt",
note = "Additional information: Later published by Society for Industrial and Applied Mathematics (2005), SIAM Journal on Applied Dynamical Systems, 4(3), pp. 459-488, ISSN 1536-0040 Sponsorship: The work of Frank Schilder is supported by EPSRC grant GR/R72020/01. Terms of use: Copyright {\textcopyright} 2005 by Society for Industrial and Applied Mathematics ",
year = "2004",
doi = "10.1137/040611240",
language = "English",
type = "WorkingPaper",
}