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On the determination of the basin of attraction of periodic orbits in three- and higher-dimensional systems

journal contribution
posted on 2023-06-08, 05:52 authored by Peter GieslPeter Giesl
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.

History

Publication status

  • Published

Journal

Journal of Mathematical Analysis and Applications

ISSN

0022-247X

Publisher

Elsevier

Issue

2

Volume

354

Page range

606-618

Pages

13.0

Department affiliated with

  • Mathematics Publications

Full text available

  • No

Peer reviewed?

  • Yes

Legacy Posted Date

2012-02-06

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