Classification of the centers, of their cyclicity and isochronicity for two classes of generalized quintic polynomial differential systems |
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| Authors: | Jaume Llibre Clàudia Valls |
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| Institution: | 1. Departament de Matemàtiques, Universitat Autònoma de Barcelona, Bellaterra, 08193, Barcelona, Catalonia, Spain
2. Departamento de Matemática, Instituto Superior Técnico, Av. Rovisco Pais, 1049-001, Lisbon, Portugal
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| Abstract: | In this paper we classify the centers localized at the origin of coordinates, the cyclicity of their Hopf bifurcation and
their isochronicity for the polynomial differential systems in
\mathbbR2{\mathbb{R}^2} of degree d that in complex notation z = x + i
y can be written as
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(z)\dot] = (l+i) z + (z`(z)])\fracd-52 (A z4+j`(z)]1-j + B z3`(z)]2 + C z2-j`(z)]3+j+D`(z)]5), \dot z = (\lambda+i) z + (z \overline{z})^{\frac{d-5}{2}} \left(A z^{4+j} \overline{z}^{1-j} + B z^3 \overline{z}^2 + C z^{2-j} \overline{z}^{3+j}+D \overline{z}^5\right), |
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