For the Hénon map $y_{n+1} = 1 - a{y}_n^{2}+bx_n$ and $x_{n+1} = y_n$, Assess the stability of the period-2 orbit when $b=0.3$ and $a=3.675$.

Question

For the Hénon map $y_{n+1} = 1 - a{y}_n^{2}+bx_n$ and $x_{n+1} = y_n$, Assess the stability of the period-2 orbit when $b=0.3$ and $a=3.675$.

I understand that the two points of the orbit must satisfy the equation $a^2y^2-a(1-b)y-a+(1-b)^2=0.$

Accordingly, I have plugged in the values for $a$ and $b$ and solved for the two points $y=0.399634$ and $y=-0.59011$.

I am now unsure how to proceed with assessing the stability of the orbit. I assume it has something to do with the Jacobian and eigenvalues but I would appreciate some guidance with regards to this.

EDIT: So I've calculated the Jacobian to be $$A=\begin{bmatrix}0&1\\b&-2ay_n\\\end{bmatrix}$$