New solvable many-body problems in the plane

We revisit an integrable (indeed, superintegrable and solvable) many-body model in-troduced almost two decades ago by Gibbons and Hermsen and by Wojciechowski, and we modify it so that its generic solutions are all isochronous (namely, completely periodic with fixed period). We then show how this model (or rather the more ba-sic dynamical system that underlies its solvable character, and other avatars of it) can be conveniently reinterpreted as (rotation-invariant) models in the plane; and we thereby present several new (solvable, isochronous and rotation-invariant) many-body problems in the plane. 1 Introduction and main results Almost two decades ago J. Gibbons and T. Hermsen [16], and almost simultaneously (and certainly independently) S. Wojciechowski [23], discussed the integrable (indeed solvable) dynamical system the equations of motion of which we write here as follows