The new Euler–Jacobi formula for points with multiplicity two provides an algebraic relation between the singular points of a polynomial vector field and their topological indices. Using this formula we obtain the configuration of the singular points together with their topological indices for the ...
The new Euler-Jacobi formula for double points provides an algebraic relation between the singular points of a polynomial vector field and their topological indices. Using this formula we obtain the configuration of the singular points together with their topological indices for the...
Polynomial differential systemsThe classical and the new Euler-Jacobi formulae for simple and double points provide an algebraic relation between the singular points of a polynomial vector field and their topological indices. Using these formulae we obtain the geometrical configuration of the singular ...
It is essential to mention that the analogous idea of avoiding the second derivative in the classical Newton’s method for solving nonlinear equations is exploited in deriving several iterative methods of various orders for solving nonlinear equations [34,35,36,37]. Moreover, some derivative-free ...