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Devil’s staircase route to chaos in a forced relaxation oscillator. (English) Zbl 0793.34028
We use one-dimensional techniques to characterize the Devil’s staircase route to chaos in a relaxation oscillator of the Van der Pol type with periodic forcing term. In particular, by using symbolic dynamics, we give the behaviour for certain range of parameters values of a Cantor set of solutions having a certain rotation set associated to a rational number. Finally, we explain the phenomena observed experimentally in the system by M. P. Kennedy, K. R. Krieg and L. O. Chua [IEEE Trans. Circuits Syst. 36, 1133-1139 (1989)] related with the appearance of secondary staircases intercalated into the primary staircases which were found by B. Van der Pol and J. Van der Mark [Nature 120 (1927)].
Reviewer: L.Alsedà

MSC:
37-XX Dynamical systems and ergodic theory
34C15 Nonlinear oscillations and coupled oscillators for ordinary differential equations
54H20 Topological dynamics (MSC2010)
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References:
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