We consider continuous $\mathrm{SL}(2,ℝ)$-cocycles over a minimal homeomorphism of a compact set $K$ of finite dimension. We show that the generic cocycle either is uniformly hyperbolic or has uniform subexponential growth.

We study the generalized random Fibonacci sequences defined by their first non-negative terms and for n≥1, Fn+2=λFn+1±Fn (linear case) and ̃Fn+2=|λ̃Fn+1±̃Fn| (non-linear case), where each ± sign is independent and either + with probability p or − with probability 1−p (0<p≤1). Our main result is that, when λ is of the form λk=2cos(π/k) for some integer k≥3, the exponential growth of Fn for 0<p≤1, and of ̃Fn for 1/k<p≤1, is almost surely positive and given by ∫0∞log x dνk, ρ(x),...