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The 16th Hilbert problem restricted to circular algebraic limit cycles

Autor
Llibre, J.; Ramirez Inostroza, Rafael; Ramirez, V.; Sadovskaia, N.
Tipus d'activitat
Article en revista
Revista
Journal of differential equations
Data de publicació
2016-04-05
Volum
260
Número
7
Pàgina inicial
5726
Pàgina final
5760
DOI
https://doi.org/10.1016/j.jde.2015.12.019 Obrir en finestra nova
URL
http://www.sciencedirect.com/science/article/pii/S0022039615006828 Obrir en finestra nova
Resum
We prove the following two results. First every planar polynomial vector field of degree S with S invariant circles is Darboux integrable without limit cycles. Second a planar polynomial vector field of degree S admits at most S-1 invariant circles which are algebraic limit cycles. In particular we solve the 16th Hilbert problem restricted to algebraic limit cycles given by circles, because a planar polynomial vector field of degree S has at most S-1 algebraic limit cycles given by circles, and ...
Paraules clau
16th Hilbert's problem, Algebraic limit circles, Darboux integrability, Invariant algebraic circles, Planar polynomial differential system, Polynomial vector fields

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