Making use of the two dimensional Taylor series of f(x,y) and g(x,y) about the fixed point, or equivalently about (ϵ,δ)=(0,0), we have \[\begin{aligned}\overset{.}{\eps...Making use of the two dimensional Taylor series of f(x,y) and g(x,y) about the fixed point, or equivalently about (ϵ,δ)=(0,0), we have \[\begin{aligned}\overset{.}{\epsilon}&=f(x_*+\epsilon ,y_*+\delta ) \\ &=f+\epsilon\frac{\partial f}{\partial x}+\delta\frac{\partial f}{\partial y}+\ldots \\ &=\epsilon\frac{\partial f}{\partial x}+\delta\frac{\partial f}{\partial y}+\ldots \\ \delta &=g(x_*+\epsilon ,y_*+\delta ) \\ &=g+\epsilon\frac{\partial g}{\partial x}+\de…
