Can a black hole horizon act as a source of Chaos?

[codebpr]

I was going through this paper where on page 5 they argue that in the given Poincare section:

Most of the orbits form regular tori, while we can also see that some tori near the saddle point of the potential collapses to become scattered plots. This saddle point corresponds to the black hole horizon, hence we confirmed that a black hole horizon works as a source of chaos.

I am a bit confused by this statement. How does the given saddle point correspond to the black hole horizon and is it necessary that it acts as a source of chaos? Any explanation would be truly beneficial!