Examples of center cyclicity bounds using the reduced Bautin depth

García, I. A. (Isaac A.)

doi:https://doi.org/10.1090/proc/13570

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Issue date

2017-09-01

Author

García, I. A. (Isaac A.)

Suggested citation

García, I. A. (Isaac A.); . (2017) . Examples of center cyclicity bounds using the reduced Bautin depth. Proceedings of the American Mathematical Society, 2017, vol. 145, p. 4363-4370. https://doi.org/10.1090/proc/13570.

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