Consider the function f defined by , where a>0. Given any initial point , it is clear that the dynamical system will have orbit

Introduce a slight perturbation to the initial condition, say, . The resulting orbit is:

So, after k iterations, these two orbits that started at neighbouring points and have separated by . Clearly, if 0<a<1, all orbits converge to zero. For a=1, all points are fixed points of the map (f is the identity map). For a>1, orbits diverge to infinity and, choosing k sufficiently large, neighbouring initial points have orbits that become arbitrarily far apart.
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