Infinite products of $2\times2$ matrices and the Gibbs properties of Bernoulli convolutions

Simple item page
dc.creatorOlivier, Eric
dc.creatorThomas, Alain
dc.date2006-07-27
dc.date.accessioned2026-07-07T07:21:02Z
dc.date.available2026-07-07T07:21:02Z
dc.descriptionWe consider the infinite sequences $(A\_n)\_{n\in\NN}$ of $2\times2$ matrices with nonnegative entries, where the $A\_n$ are taken in a finite set of matrices. Given a vector $V=\pmatrix{v\_1\cr v\_2}$ with $v\_1,v\_2>0$, we give a necessary and sufficient condition for $\displaystyle{A\_1... A\_nV\over|| A\_1... A\_nV||}$ to converge uniformly. In application we prove that the Bernoulli convolutions related to the numeration in Pisot quadratic bases are weak Gibbs.
dc.identifierhttps://arxiv.org/abs/math/0607704
dc.identifierhttp://arxiv.org/abs/math/0607704
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/115162
dc.subjectNumber Theory
dc.subject28A12; 11A67; 15A48
dc.titleInfinite products of $2\times2$ matrices and the Gibbs properties of Bernoulli convolutions
dc.typetext

Files

Collections

arXiv