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On the determination of the basin of attraction of periodic orbits in three- and higher-dimensional systems
The determination of the basin of attraction of a periodic orbit can be achieved using a Lyapunov function. A Lyapunov function can be constructed by approximation of a first-order linear PDE for the orbital derivative via meshless collocation. However, if the periodic orbit is only accessible numerically, a different method has to be used near the periodic orbit. Borg's criterion provides a method to obtain information about the basin of attraction by measuring whether adjacent solutions approach each other with respect to a Riemannian metric. Using a numerical approximation of the periodic orbit and its first variation equation, a suitable Riemannian metric is constructed.
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Publication status
- Published
Journal
Journal of Mathematical Analysis and ApplicationsISSN
0022-247XPublisher
ElsevierExternal DOI
Issue
2Volume
354Page range
606-618Pages
13.0Department affiliated with
- Mathematics Publications
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- No
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- Yes
Legacy Posted Date
2012-02-06Usage metrics
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