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Problem: Consider the autonomous ODE system \begin{align*} \dot{x} &= (1-x) (z-xy)\\ \dot{y} &= \tfrac 1 2 y^2 - (a+xy)(1-y) \\ \dot{z} &= \tfrac 1 2 z^2 - \tfrac 1 2 y^2 + (a+xy)z \end{...

In a book, i have read a remark which says that the center manifold of an equilibrium point of a differential equation is not unique in general but is unique in the class of analytic manifold. The ...