A topological method for rigorously computing periodic orbits using Fourier modes

Anthony W. Baker; Michael Dellnitz; Oliver Junge

A topological method for rigorously computing periodic orbits using Fourier modes

Anthony W. Baker
, Michael Dellnitz
, Oliver Junge

Universität Paderborn

Research output: Contribution to journal › Review article › peer-review

8 Scopus citations

Abstract

We present a technique for the rigorous computation of periodic orbits in certain ordinary differential equations. The method combines set oriented numerical techniques for the computation of invariant sets in dynamical systems with topological index arguments. It not only allows for the proof of existence of periodic orbits but also for a precise (and rigorous) approximation of these. As an example we compute a periodic orbit for a differential equation introduced in [2].

Original language	English
Pages (from-to)	901-920
Number of pages	20
Journal	Discrete and Continuous Dynamical Systems- Series A
Volume	13
Issue number	4
State	Published - Nov 2005
Externally published	Yes

Keywords

Computer assisted proof
Dynamical system
Periodic orbit
Set oriented methods

Cite this

@article{1bebf6739ec2476890217048dcf9cc66,

title = "A topological method for rigorously computing periodic orbits using Fourier modes",

abstract = "We present a technique for the rigorous computation of periodic orbits in certain ordinary differential equations. The method combines set oriented numerical techniques for the computation of invariant sets in dynamical systems with topological index arguments. It not only allows for the proof of existence of periodic orbits but also for a precise (and rigorous) approximation of these. As an example we compute a periodic orbit for a differential equation introduced in [2].",

keywords = "Computer assisted proof, Dynamical system, Periodic orbit, Set oriented methods",

author = "Baker, \{Anthony W.\} and Michael Dellnitz and Oliver Junge",

year = "2005",

month = nov,

language = "English",

volume = "13",

pages = "901--920",

journal = "Discrete and Continuous Dynamical Systems- Series A",

issn = "1078-0947",

publisher = "American Institute of Mathematical Sciences",

number = "4",

}

TY - JOUR

T1 - A topological method for rigorously computing periodic orbits using Fourier modes

AU - Baker, Anthony W.

AU - Dellnitz, Michael

AU - Junge, Oliver

PY - 2005/11

Y1 - 2005/11

N2 - We present a technique for the rigorous computation of periodic orbits in certain ordinary differential equations. The method combines set oriented numerical techniques for the computation of invariant sets in dynamical systems with topological index arguments. It not only allows for the proof of existence of periodic orbits but also for a precise (and rigorous) approximation of these. As an example we compute a periodic orbit for a differential equation introduced in [2].

AB - We present a technique for the rigorous computation of periodic orbits in certain ordinary differential equations. The method combines set oriented numerical techniques for the computation of invariant sets in dynamical systems with topological index arguments. It not only allows for the proof of existence of periodic orbits but also for a precise (and rigorous) approximation of these. As an example we compute a periodic orbit for a differential equation introduced in [2].

KW - Computer assisted proof

KW - Dynamical system

KW - Periodic orbit

KW - Set oriented methods

UR - https://www.scopus.com/pages/publications/28444446312

M3 - Review article

AN - SCOPUS:28444446312

SN - 1078-0947

VL - 13

SP - 901

EP - 920

JO - Discrete and Continuous Dynamical Systems- Series A

JF - Discrete and Continuous Dynamical Systems- Series A

IS - 4

ER -

A topological method for rigorously computing periodic orbits using Fourier modes

Abstract

Keywords

Other files and links

Fingerprint

Cite this