First of all, hello.
I'm having trouble determining whether fixed points are stable or unstable.
I have a recursion function: \begin{align*} f_{\alpha,\gamma} \left( \begin{array}{c} t\\ v \end{array}\right)= \left( \begin{array}{c} (t+v)mod(2\pi)\\ \alpha v-\gamma cos(t+v)) \end{array}\right) \end{align*} and the fixed points: $(t^*,v^*)=(\arccos\left(\frac{2k\pi(\alpha-1)}{\gamma}\right),2k\pi)$
Can anyone tell me how to determine if a fixed point is stable or unstable?