One fact is here taken for granted, and I wonder whether this is a necessary outcome in this setup, or whether this is an additional assumption: after some time the system ejects one body that flies off into the infinite distance, leaving behind a binary system. This is a dramatic transition in the system's dynamics, which helps understand the criterion of "irreversibility" that they use: — SophistiCat

:up: Good point.

"In mathematics, a dynamical system is time-reversible if the forward evolution is one-to-one" — jgill

Well, your wiki reference gives rather more succinct definitions, though they may require some unpacking. — SophistiCat

I don't wish to belabor the point, and, to keep it elementary and overly simplistic, avoiding the unpacking, the example

${{F}_{n}}(z)=f\left( {{F}_{n-1}}(z) \right),\text{ }{{F}_{1}}(z)=f(z)$,
$f(z)={{z}^{2}}+1$

shows the difficulty in reversing steps in a dynamical system, an expansion, this one very well behaved. The paper in question is far more sophisticated and I can't argue in that advanced physics environment. Although it makes more sense to deal with system reversibility than pointwise reversibility.