Year: 2001
Type: article
Abstract: Solutions to the random Fibonacci recurrence x n + 1 = x n ±β x n -1 decrease (increase) exponentially, x n ~exp (λ n ), for sufficiently small (large) β. In the limits β→0 and β→ ∞ , we expand the Lyapunov exponent λ(β) in powers of β and β -1 , respectively. For the classical case of β = 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 r .
Authors: Clément Sire, Paul L Krapivsky
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
Funder: National Science Foundation
OpenAlex ID: W2081078482