  It is known that certain types of particle motion near black hole horizons
are chaotic while it has been proposed the existence of a universal bound for
their Lyapunov exponent. We discuss the relation between chaos and inaffinity
in presence of black hole and cosmological horizons. We argue that although a
relation between the Lyapunov exponent and the generalized surface gravity
appears naturally, in general there is no reason for the Lyapunov exponent of
classical trajectories to be bounded in generic spacetimes with horizon.
Moreover, we show that the de Sitter spacetime and cosmological horizons act as
a nest of chaos in holography and we find that the Lyapunov exponent of the
trajectories is related to the inaffinity in the same way for both cosmological
and black hole horizons. This suggests that there is no distinction by the
Lyapunov exponent between maximal chaos of black hole and cosmological
horizons.
