Bifurcation of critical periods of polynomial systems

We describe a general approach to studying bifurcations of critical periods based on a complexification of the system and algorithms of computational algebra. Using this approach we obtain upper bounds on the number of critical periods of several families of cubic systems. In some cases we overcome...

Full description

Saved in:
Bibliographic Details
Published in:Journal of Differential Equations 2015-10, Vol.259 (8), p.3825-3853
Main Authors: Ferčec, Brigita, Levandovskyy, Viktor, Romanovski, Valery G., Shafer, Douglas S.
Format: Article
Language:English
Subjects:
Bifurcations
Critical periods
Isochronicity
Polynomial systems
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We describe a general approach to studying bifurcations of critical periods based on a complexification of the system and algorithms of computational algebra. Using this approach we obtain upper bounds on the number of critical periods of several families of cubic systems. In some cases we overcome the problem of nonradicality of a relevant ideal by moving it to a subalgebra generated by invariants of a group of linear transformations.
ISSN:0022-0396
1090-2732
DOI:10.1016/j.jde.2015.05.004