On the average growth of random Fibonacci sequences.
Équidistribution presque partout modulo 1 de suites oscillantes perturbées
Équidistribution presque partout modulo 1 de suites oscillantes perturbées - II : cas liouvillien unidimensionnel
On subsequences of convergents to a quadratic irrational given by some numerical schemes
Given a quadratic irrational , we are interested in how some numerical schemes applied to a convenient function provide subsequences of convergents to . We investigate three numerical schemes: secant-like methods and formal generalizations, which lead to linear recurring subsequences; the false position method, which leads to arithmetical subsequences of convergents and gives some interesting series expansions; Newton’s method, for which we complete a result of Edward Burger [] about the existence...
Almost-sure growth rate of generalized random Fibonacci sequences
We study the generalized random Fibonacci sequences defined by their first non-negative terms and for ≥1, +2= +1± (linear case) and +2=| +1± | (non-linear case), where each ± sign is independent and either + with probability or − with probability 1− (0<≤1). Our main result is that, when is of the form =2cos(/) for some integer ≥3, the exponential growth of for 0<≤1,...
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