Iterated networks and the spectra of renormalizable electromechanical systems

Barnsley, M. F.; Morley, T. D.; Vrscay, E. R.

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Iterated networks and the spectra of renormalizable electromechanical systems

Date

1985

Authors

Barnsley, M. F.

Morley, T. D.

Vrscay, E. R.

Abstract

Beginning with an LRC network with impedance function Z(Ω), a sequence of iterated networks Nk with impedance functions Z‡k(Ω), k= 1, 2, 3,..., is introduced. The asymptotic comportment of Z‡k(Ω) and the spectra of Nk are analyzed in terms of the Julia set of Z. An example is given of an iterated network associated with a cascade of period-doubling bifurcations.