Suppose that I have a one dimensional dynamical system with the following characteristic:
There are three fixed points, out of which the one of the far "left" and the one on the far "right" are stable, while the one in the "middle" is unstable.
I am asking the following question:
Suppose that a particle starts near the unstable "middle" fixed point, is it possible to know for every repetition of the experiment where will my particle end-up? Or perhaps is there a method I could approximate the probability of ending-up on the "left" or the "right" stable fixed point?
I searched a bit around the bibliography and the only thing similar to what I am looking for is "splitting probabilities" but that is not helpful in my case.
Thanks.