Examples of center cyclicity bounds using the reduced Bautin depth

Thumbnail
View/Open
Issue date
2017-09-01
Author
García, I. A. (Isaac A.)
Impact

Google Scholar logo  Google Scholar
Share
Export to Mendeley
Metadata
Show full item record
Abstract
There is a method for bounding the cyclicity of nondegenerate monodromic singularities of polynomial planar families of vector fields Xλ which can work even in case that the Poincar´e first return map has associated a non-radical Bautin ideal B. The method is based on the stabilization of the integral
closures of an ascending chain of polynomial ideals in the ring of polynomials in the parameters λ of the family that stabilizes at B. In this work we use computational algebra methods to provide an explicit example in which the classical procedure to find the Bautin depth of B fails but the new approach is successful.
URI
http://hdl.handle.net/10459.1/60208
DOI
https://doi.org/10.1090/proc/13570
Is part of
Proceedings of the American Mathematical Society, 2017, vol. 145, p. 4363-4370
Collections