Random Fibonacci Sequences

Details Random Fibonacci Sequences Random Fibonacci Sequences

2001-06-22

arxiv.org/abs/cond-mat/0106457v1

J. Phys. A 34, 9065 (2001)

Physics

Condensed Matter

Statistical Mechanics

11 Pages (Multi-Column); 3 EPS Figures ; Submitted to J. Phys. A

Scientific paper

10.1088/0305-4470/34/42/322

Solutions to the random Fibonacci recurrence x_{n+1}=x_{n} + or - Bx_{n-1} decrease (increase) exponentially, x_{n} = 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 $\beta=1$ we obtain exact non-perturbative results. In particular, an invariant measure associated with Ricatti variable r_n=x_{n+1}/x_{n} is shown to exhibit plateaux around all rational.

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