Isochronous Cosmologies

The possibility has been recently demonstrated to manufacture (nonrelativistic, Hamiltonian) many-body problems which feature an isochronous time evolution with an arbitrarily assigned period $T$ yet mimic with good approximation, or even exactly, any given many-body problem (within a large, physically relevant, class) over times $\tilde{T}$ which may also be arbitrarily large (but of course such that $\tilde{T}