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Center problem for systems with two monomial nonlinearities

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Issue date
2016
Author
Gasull i Embid, Armengol
Giné, Jaume
Torregrosa, Joan
Suggested citation
Gasull i Embid, Armengol; Giné, Jaume; Torregrosa, Joan; . (2016) . Center problem for systems with two monomial nonlinearities. Communications on Pure and Applied Analysis, 2016, vol. 15, núm. 2, p. 577-598. https://doi.org/10.3934/cpaa.2016.15.577.
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Abstract
We study the center problem for planar systems with a linear center at the origin that in complex coordinates have a nonlinearity formed by the sum of two monomials. Our first result lists several centers inside this family. To the best of our knowledge this list includes a new class of Darboux centers that are also persistent centers. The rest of the paper is dedicated to try to prove that the given list is exhaustive. We get several partial results that seem to indicate that this is the case. In particular, we solve the question for several general families with arbitrary high degree and for all cases of degree less or equal than 19. As a byproduct of our study we also obtain the highest known order for weak-foci of planar polynomial systems of some given degrees.
URI
http://hdl.handle.net/10459.1/58414
DOI
https://doi.org/10.3934/cpaa.2016.15.577
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Communications on Pure and Applied Analysis, 2016, vol. 15, núm. 2, p. 577-598
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