caa a22 4500 445869437 CHVBK 20180317145507.0 cr unu---uuuuu 170323e20110801xx s 000 0 eng 10.1007/s00605-010-0230-z doi (NATIONALLICENCE)springer-10.1007/s00605-010-0230-z Nombre de branchement d'un pseudogroupe [Elektronische Daten] [Fernando Alcalde Cuesta, María Fernández de Córdoba] Lyons has defined an average number of branches per vertex of an infinite locally finite rooted tree. This number has an important role in several probabilistic processes such as random walk and percolation. In this paper, we extend the notion of branching number to any measurable graphed pseudogroup of finite type acting on a probability space. We prove that such a pseudogroup is Liouvillian (i.e. almost every orbit does not admit non-constant bounded harmonic functions) if its branching number is equal to 1. In order to prove that this actually generalizes results of C. Series and V. Kaimanovich on equivalence relations with polynomial and subexponential growth, we describe an example of minimal lamination whose holonomy pseudogroup has exponential growth and branching number equal to 1. Springer-Verlag, 2010 Graphed pseudogroup nationallicence Lamination nationallicence Branching number nationallicence Liouville property nationallicence Amenability nationallicence Alcalde Cuesta Fernando Departamento de Xeometría e Topoloxía, Universidade de Santiago de Compostela, 15872, Santiago de Compostela, Espagne aut Fernández de Córdoba María Departamento de Xeometría e Topoloxía, Universidade de Santiago de Compostela, 15872, Santiago de Compostela, Espagne aut Monatshefte für Mathematik Springer Vienna 163/4(2011-08-01), 389-414 0026-9255 163:4<389 2011 163 605 https://doi.org/10.1007/s00605-010-0230-z text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00605-010-0230-z text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Alcalde Cuesta Fernando Departamento de Xeometría e Topoloxía, Universidade de Santiago de Compostela, 15872, Santiago de Compostela, Espagne aut NATIONALLICENCE 700 1- Fernández de Córdoba María Departamento de Xeometría e Topoloxía, Universidade de Santiago de Compostela, 15872, Santiago de Compostela, Espagne aut NATIONALLICENCE 773 0- Monatshefte für Mathematik Springer Vienna 163/4(2011-08-01), 389-414 0026-9255 163:4<389 2011 163 605 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer