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TitleSymbolic computation and the cyclicity problem for singularities
Author(s) D.S. Shafer
TypeArticle in Journal
AbstractWe show how methods of computational commutative algebra are employed to investigate the local 16th Hilbert Problem, which is to find an upper bound on the number of limit cycles that can bifurcate from singularities in families of polynomial systems of differential equations on R 2 , and is one step in a program for solving the full 16th Hilbert Problem. We discuss an extension of a well-known theorem, and illustrate the concepts and methods with concrete examples.
KeywordsCyclicity problem, Polynomial systems of nonlinear differential equations, Bautin ideal, Computational commutative algebra
ISSN0747-7171
URL http://www.sciencedirect.com/science/article/pii/S0747717111002306
LanguageEnglish
JournalJournal of Symbolic Computation
Volume47
Number10
Pages1140 - 1153
Year2012
NoteSymbolic Computation and its Applications
Edition0
Translation No
Refereed No
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