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Twist periodic solutions in the relativistic driven harmonic oscillator. (English) Zbl 1470.34121

Summary: We study the one-dimensional forced harmonic oscillator with relativistic effects. Under some conditions of the parameters, the existence of a unique stable periodic solution is proved which is of twist type. The results depend on a Twist Theorem for nonlinear Hill’s equations which is established and proved here.

MSC:

34C25 Periodic solutions to ordinary differential equations
37C27 Periodic orbits of vector fields and flows
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