2 N ov 2 00 4 On the Gibbs properties of Bernoulli convolutions related to β - numeration in multinacci bases
نویسندگان
چکیده
We consider infinitely convolved Bernoulli measures (or simply Bernoulli convolutions) related to the β-numeration. A matrix decomposition of these measures is obtained in the case when β is a PV number. We also determine their Gibbs properties for β being a multi-nacci number, which makes the multifractal analysis of the corresponding Bernoulli convolution possible.
منابع مشابه
On the Gibbs properties of Bernoulli convolutions
We consider infinitely convolved Bernoulli measures (or simply Bernoulli convolutions) related to the β-numeration. A matrix decomposition of these measures is obtained in the case when β is a PV number. We also determine their Gibbs properties for β being a multinacci number, which makes the multifractal analysis of the corresponding Bernoulli convolution possible.
متن کاملWeak Gibbs property and systems of numeration
Weak Gibbs property and systems of numeration parÉric OLIVIER et Alain THOMAS Résumé. Nousétudions les propriétés d'autosimilarité et la nature gibbsienne de certaines mesures definies sur l'espace produit Ω r := {0, 1,. .. , r−1} N. Cet espace peutêtre identifiéà l'intervalle [0, 1] au moyen de la numération en base r. Le dernier paragraphe concerne la convolution de Bernoulli en base β = 1+ √...
متن کاملOn Properties of Representations in Certain Linear Numeration Systems
Given a ≥ b, let G0 = 1, G1 = a+ 1, and Gn+2 = aGn+1 + bGn for n ≥ 0. For each choice of a and b, we have a linear recurrence that defines a numeration system. Every positive integer n may be written as the sum of the Gn, with alphabet A = {0, 1, . . . a}, in one or more different ways. Let R(a,b)(n) be the function that counts the number of distinct representations of an integer as a sum of th...
متن کاملCalculating the Numbers of Representations and the Garsia Entropy in Linear Numeration Systems
Given a ≥ b, let G0 = 1, G1 = a + 1, and Gn+2 = aGn+1 + bGn for n ≥ 0. For each choice of a and b, we have a linear recurrence that defines a numeration system. Every positive integer n may be written as the sum of the Gn, with alphabet A = {0, 1, . . . , a}, in one or more different ways. Let R(a,b)(n) be the function that counts the number of distinct representations of an integer as a sum of...
متن کامل2 7 Ju l 2 00 6 Infinite products of 2 × 2 matrices and the Gibbs properties of Bernoulli convolutions
Nevertheless the normalized rows of Pn(ω) in general do not converge: suppose for instance that all the matrices in M are positive but do not have the same positive normalized left-eigenvector, let Lk such that LkMk = ρkLk. For any positive matrix M , the normalized rows of MM0 n converge to L0 and the ones of MM1 n to L1. Consequently we can choose the sequence (nk)k∈N sufficiently increasing ...
متن کامل