Solution
= Solution
The <fixed-point multiplier> decreases continuously with $\gamma$ and first reaches the <unit circle> at $-1$. Solving $1-\gamma_*(1-\beta/\alpha)=-1$ gives
$$
\boxed{\gamma_*=\frac{2\alpha}{\alpha-\beta}>2.}
$$
It is stable for $1<\gamma<\gamma_*$ and unstable for $\gamma>\gamma_*$. At the critical value <linear stability> is inconclusive. The crossing at $-1$ is the local signature of a <period-doubling bifurcation>, rather than a crossing through $+1$.