Revisit "example of an unstable fixed point for which the linearized dynamics are stable"

Question

I am reading the following discussion:

example of an unstable fixed point for which the linearized dynamics are stable

The above discussion is for the vector field (continuous time).

Is there an example for the discrete time (map)?

$$x_{n+1} = f(x_n)$$

I know that for the linearization case $$x_{n+1} = Ax_n,$$ if $|\lambda(A)| <1$, it is stable; $|\lambda(A)| >1$, unstable.

Is there an example of a map which has a fixed point stable in the linearization approximation but unstable in the original nonlinear system?