Various aspects of differential equations having a complete set of independent first integrals

Details Various aspects of differential equations having a complete set of independent first integrals Various aspects of differential equations having a complete set of independent first integrals

2011-06-13

arxiv.org/abs/1106.2563v1

Mathematics

Dynamical Systems

Scientific paper

In this paper we study the differential equations in $D\subseteq \R^{2N}$ having a complete set of independent first integrals. In particular we study the case when the first integrals are \[f_\nu=(Ax_\nu+By_\nu)^2+\displaystyle\sum_{j=1}^{N}\dfrac{(x_\nu y_j-x_jy_\nu)^2}{a_\nu-a_j},\]for $\nu=1,...,N,$ where $A,B$ and $a_1

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