I have conducted simulations of a discrete dynamical system. I know the fixed points of the system and which of them are attractive. According to the simulations, I obtain that certain fixed points that are not locally attractive can have basins of attraction away from the point.

I would like to know whether it is possible or it is just rounding errors.

Thank you!

Sorry, I think I can rise the question in a more precise way:

Let $x \in \mathbb{R}^n$ be an unstable fixed point of the discrete dynamical system $\mathcal{G}$. There may be a set $A \subset \mathbb{R}^n$ with non-zero Lebesgue measure such that $\forall y \in A, lim_{n\rightarrow \infty} \mathcal{G}^n(y) = x$ ?