What is the Kronecker index in dynamical systems?

Onias
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Hello all,
I was wondering what is the Kronecker index in relation to dynamical systems. For instance a sample question would be find the Kronecker indices ind(0,x-F(x)) and ind(inf,x-F(x)) for the dynamical system {(dx/dt)=g(x,y),(dy/dt)=h(x,y)}. Thanks in advance.
 
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Thread 'Direction Fields and Isoclines'

Thread 'Direction Fields and Isoclines'

I sketched the isoclines for $$ m=-1,0,1,2 $$. Since both $$ \frac{dy}{dx} $$ and $$ D_{y} \frac{dy}{dx} $$ are continuous on the square region R defined by $$ -4\leq x \leq 4, -4 \leq y \leq 4 $$ the existence and uniqueness theorem guarantees that if we pick a point in the interior that lies on an isocline there will be a unique differentiable function (solution) passing through that point. I understand that a solution exists but I unsure how to actually sketch it. For example, consider a...
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