Iterated networks and the spectra of renormalizable electromechanical systems (Q578711)

Beginning with an LRC network with impedance function Z(\(\omega)\), a sequence of iterated networks \(N_ k\) with impedance functions \(Z^{ok}(\omega)\), \(k=1,2,3,...\), is introduced. The asymptotic comportment of \(Z^{ok}(\omega)\) and the spectra of \(N_ k\) 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.