Centers and Isochronous Centers for Two Classes of Generalized Seventh and Ninth Systems
2010; Springer Science+Business Media; Volume: 22; Issue: 4 Linguagem: Inglês
10.1007/s10884-010-9175-0
ISSN1572-9222
Autores Tópico(s)Quantum chaos and dynamical systems
ResumoWe classify new classes of centers and of isochronous centers for polynomial differential systems in $${\mathbb R^2}$$ of arbitrary odd degree d ≥ 7 that in complex notation z = x + i y can be written as $$\dot z = (\lambda+i) z + (z \overline z)^{\frac{d-7-2j}2} \left(A z^{5+j} \overline z^{2+j} + B z^{4+j} \overline z^{3+j} + C z^{3+j} \overline z^{4+j}+D \overline z^{7+2j} \right),$$ where j is either 0 or $${1, \lambda \in \mathbb R}$$ and $${A,B,C \in \mathbb C }$$ . Note that if j = 0 and d = 7 we obtain a special case of seventh polynomial differential systems which can have a center at the origin, and if j = 1 and d = 9 we obtain a special case of ninth polynomial differential systems which can have a center at the origin.
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