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We study the periodic solutions of the scalar delay equation \[\dot{x}(t)=f(x(t),x(t-1)), \] where $f$, regular enough, satisfies even-oddsymmetries and is strictly monotone in the delayed component. Our results fullycharacterize the set of periodic solutions and their stability in terms of atime map defined for a planar ordinary differential equation. The presentationis the uniqueness counterpart of existence results developed by Kaplan andYorke in 1974.

Periodic orbits of delay equations with monotone feedback and even-odd symmetry