I am currently struggling to find a closed form solution for a recurrence relation and don't know where to start. I have worked with linear homogenous first and second-order relations before but this is unlike anything I have seen. Suggestions would be greatly appreciated.
$$k_{t+1}=A(1-\alpha)(1-\beta)g^tk_t^\beta$$
where $\alpha$ and $\beta$ are strictly between $0$ and $1$, $t>0$, $k_1>0$, $g$ is a growth rate and $A$ is a positive real constant.