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Abstract
An isochronous dynamical system is characterized by the existence of an open domain of initial data such that all motions evolving from it are completely periodic with a fixed period (independent of the initial data). Taking advantage of a recently introduced trick, a (quite large) class of such systems is identified, with equations of motion ‘of Newtonian type.’ Subcases are exhibited in which the equations of motion are Hamiltonian, and/or are interpretable as the equations of motion of a many-body problem, possibly with one- and two-body forces only, possibly invariant under rotations and/or translations, possibly constituting a one-parameter deformation of a classical physical problem (such as the many-body gravitational problem in ordinary three-dimensional space).