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Characteristic multipliers and stability of symmetric periodic solutions of $$\dot x(t)=g(x(t-1))$$. (English) Zbl 0672.34069
The equation (1) $$\dot x(t)=g(x(t-1))$$ is considered where g is an odd and monotone nonlinear function. It is proved that for a certain class of such functions the nontrivial characteristic multipliers of any periodic solution of (1) satisfying $$x(t)=-x(t-2)$$, $$t\in R$$, are all strictly inside the unit circle.