Isochronous Dynamical System and Diophantine Relations I

We identify a solvable dynamical system — interpretable to some extent as many-body problem and point out that for an appropriate assignment of its parameters it is entirely isochronous, namely all nonsingular solutions are completely periodic (i.e., in degrees freedom) with the same fixed period (independent initial data). then equilibrium configurations investigate behavior their neighborhood. thereby certain matrices arbitrary order whose eigenvalues rational numbers: Diophantine finding.