Numerical computation of invariant circles of maps

I. G. Kevrekidis, R. Aris, L. D. Schmidt, S. Pelikan

Research output: Contribution to journalArticle

44 Scopus citations

Abstract

A method for the numerical computation of invariant circles of maps is presented, along with appropriate techniques for its implementation. The method involves solution of a functional equation by discretization and Newton iteration. The resulting algorithm is applied to a map of the cylinder and some examples of bifurcations of invariant circles are illustrated. Generalization of the method to the computation of invariant circles in more than two dimensions as well as sections of invariant tori is discussed.

Original languageEnglish (US)
Pages (from-to)243-251
Number of pages9
JournalPhysica D: Nonlinear Phenomena
Volume16
Issue number2
DOIs
StatePublished - Jun 1985

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Condensed Matter Physics
  • Applied Mathematics

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    Kevrekidis, I. G., Aris, R., Schmidt, L. D., & Pelikan, S. (1985). Numerical computation of invariant circles of maps. Physica D: Nonlinear Phenomena, 16(2), 243-251. https://doi.org/10.1016/0167-2789(85)90061-2