Numerical computation of invariant circles of maps

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

doi:10.1016/0167-2789(85)90061-2

Numerical computation of invariant circles of maps

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

Chemical & Biological Engineering

Research output: Contribution to journal › Article › peer-review

48 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 language	English (US)
Pages (from-to)	243-251
Number of pages	9
Journal	Physica D: Nonlinear Phenomena
Volume	16
Issue number	2
DOIs	https://doi.org/10.1016/0167-2789(85)90061-2
State	Published - Jun 1985

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Mathematical Physics
Condensed Matter Physics
Applied Mathematics

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10.1016/0167-2789(85)90061-2

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title = "Numerical computation of invariant circles of maps",

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.",

author = "Kevrekidis, {I. G.} and R. Aris and Schmidt, {L. D.} and S. Pelikan",

note = "Funding Information: tThis work is partially supported by NSF under grant no. CPE 8313497. *Present address: Department of Mathematics, University of Cincinnati.",

year = "1985",

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AU - Kevrekidis, I. G.

AU - Aris, R.

AU - Schmidt, L. D.

AU - Pelikan, S.

N1 - Funding Information: tThis work is partially supported by NSF under grant no. CPE 8313497. *Present address: Department of Mathematics, University of Cincinnati.

PY - 1985/6

Y1 - 1985/6

N2 - 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.

AB - 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.

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Numerical computation of invariant circles of maps

Abstract

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