Periodic motions galore: how to modify nonlinear evolution equations so that they feature a lot of periodic solutions
F Calogero, Jean–Pierre Françoise · 2002
A simple trick is illustrated, whereby nonlinear evolution equations can be modified so that they feature a lot – or, in some cases, only – periodic solutions. Several examples (ODEs and PDEs) are exhibited. 1 Introduction and outline of results Many natural phenomena (in physics, chemistry, biology, physiology,...), and also several phenomena pertaining to the social sciences (for instance in economics), display a cyclic behavior. Hence, to the extent they can be described by mathematical models, they call into play evolution equations that feature periodic solutions. Practitioners of such