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.   We discuss the genericity of some multiplicity results for periodically perturbed autonomous first- and second-order ODEs on manifolds.¶In particular, the genericity of the following property is investigated: if the differentiable manifold M is compact, then the equation  π=h(x,)+f(t,x,) on M has |χ(M)| geometrically distinct T-periodic solutions for any small enough T-periodic perturbing function f.

A remark on the genericity of multiplicity results for forced oscillations on manifolds