Random Fibonacci Sequences
Abstract
Solutions to the random Fibonacci recurrence xn+1=xn + or - Bxn-1 decrease (increase) exponentially, xn = exp(lambda n), for sufficiently small (large) B. In the limits B --> 0 and B --> infinity, we expand the Lyapunov exponent lambda(B) in powers of B and B-1, respectively. For the classical case of β=1 we obtain exact non-perturbative results. In particular, an invariant measure associated with Ricatti variable rn=xn+1/xn is shown to exhibit plateaux around all rational.
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