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

Giesl, Peter (2009) On the determination of the basin of attraction of periodic orbits in three- and higher-dimensional systems. Journal of Mathematical Analysis and Applications, 354 (2). pp. 606-618. ISSN 0022-247X

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Abstract

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.

Item Type: Article
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Depositing User: Peter Giesl
Date Deposited: 06 Feb 2012 20:18
Last Modified: 10 Jul 2012 09:26
URI: http://sro.sussex.ac.uk/id/eprint/25318
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