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## On the upper bound of the number of functionally independent focal quantities of the Lyapunov differential system

Authors: Popa Mihail, Pricop Victor

### Abstract

Denote by $N_1=2\sum\limits_{i=1}^{\ell}(m_i+1)+2$ the maximal possible number of non-zero coefficients of the Lyapunov differential system $\dot{x}= y+\sum\limits_{i=1}^{\ell}P_{m_i}(x,y)$, \linebreak $\dot{y}= -x+\sum\limits_{i=1}^{\ell}Q_{m_i}(x,y)$, where $P_{m_i}$ and $Q_{m_i}$ are homogeneous polynomials of degree $m_i$ with respect to $x$ and $y$, and \$1