Matrix semigroups and applications
type: Dataset
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.
landing page: https://theses.hal.science/tel-00782789
identifier: NNT: 2012PA112373
keyword: -adics-developpements
keyword: automata
keyword: automate
keyword: continued-fraction
keyword: critical-exponant
keyword: decidabilite
keyword: decidability
keyword: developpements--adiques
keyword: dimension-de-hausdorff
keyword: ensemble-limite
keyword: espace-hyperbolique
keyword: exposant-critique
keyword: fraction-continue
keyword: hausdorff-dimension
keyword: hyperbolic-space
keyword: infoeu-reposemanticsdoctoralthesis
keyword: isometries
keyword: langage-rationnel
keyword: limit-set
keyword: mathmath-gmmathematics-mathgeneral-mathematics-mathgm
keyword: regular-langage
keyword: semi-groupes
keyword: semigroups
keyword: theses
issued: 2026-05-14T19:47:07.037697
modified: 2026-05-14T19:47:07.037703
language: fr
contact point: Organization
  fn: CCSD

test_moissonnage_selune
type: Agent

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