A system of degree four with an invariant triangle and at least three small amplitude limit cycles | Zendy

Zhenhai Liu | Zendy; Eduardo Sáez | Zendy; Iván Szántó | Zendy

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A system of degree four with an invariant triangle and at least three small amplitude limit cycles

Author(s) -

Zhenhai Liu,

Eduardo Sáez,

Iván Szántó

Publication year - 2010

Publication title -

electronic journal of qualitative theory of differential equations

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.524

H-Index - 33

ISSN - 1417-3875

DOI - 10.14232/ejqtde.2010.1.69

Subject(s) - mathematics , invariant (physics) , amplitude , degree (music) , limit (mathematics) , mathematical analysis , pure mathematics , mathematical physics , physics , quantum mechanics , acoustics

We show the existence of a polynomial system of degree four having three real invariant straight lines forming a triangle with at least three small am- plitude limit cycles in the interior. Also, we obtain the necessary and sufficient conditions for the critical point at the interior of the bounded region to be a center.

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