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Taming chaotic dynamics with weak periodic perturbations. (English) Zbl 0968.37508
Summary: The possibility of eliminating chaos in a dynamical system or of decreasing the leading Liapunov exponent by applying a weak periodic external forcing to the system is demonstrated through the example of a periodically driven pendulum. The applications of the external forcing also results in other striking changes in the dynamics such as a stabilization of narrow subharmonic steps and the achievement of very low winding numbers.

MSC:
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
34C23 Bifurcation theory for ordinary differential equations
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