Matrix semigroups and applications
type: Dataset
contact point: Organization
  fn: CCSD
keyword: exposant-critique
keyword: langage-rationnel
keyword: theses
keyword: regular-langage
keyword: critical-exponant
keyword: mathmath-gmmathematics-mathgeneral-mathematics-mathgm
keyword: dimension-de-hausdorff
keyword: -adics-developpements
keyword: continued-fraction
keyword: hyperbolic-space
keyword: infoeu-reposemanticsdoctoralthesis
keyword: developpements--adiques
keyword: automate
keyword: automata
keyword: espace-hyperbolique
keyword: semi-groupes
keyword: limit-set
keyword: ensemble-limite
keyword: decidability
keyword: fraction-continue
keyword: decidabilite
keyword: semigroups
keyword: isometries
keyword: hausdorff-dimension
landing page: https://theses.hal.science/tel-00782789
description: We study matrix semigroups with different point of view that overlaps. The growth point of view seems to be related with the geometric point of view : we partially generalize to the semigroups a theorem on groups of Patterson-Sullivan-Paulin, that give the equality between the critical exponent and the Hausdorff dimension of the limit set. We obtain this in the general framework of isometries of a Gromov-hyperbolic space, and our proof give also others new results. The computer science point of view is also related to the growth, since we obtain a way to calculate exact values of critical exponents of somes β-adic development semigroups, from a notion of automatic semigroups that we introduce. Furthermore this point of view give a lot of information on these semigroups. This notion of growth shows to be also related to conjectures on continued fractions like Zaremba’s one. And by studing some matrix semigroups we were able to prove some results on bounded periodic continued fractions, doing a little step in the resolution of a conjecture of McMullen.
identifier: NNT: 2012PA112373
issued: 2026-05-14T19:47:07.037697
language: fr
modified: 2026-05-14T19:47:07.037703

test_moissonnage_selune
type: Agent

Matrix semigroups and applications
type: Distribution
access URL: https://theses.hal.science/tel-00782789
format: HTML
issued: 2026-05-14T19:47:07.126786
modified: 2026-05-14T19:47:06.989556