Séminaires et Congrès 2011; 251 pp; softcover Number: 20 ISBN10: 2856293123 ISBN13: 9782856293126 List Price: US$60 Member Price: US$48 Order Code: SECO/20
 This volume, which contains a selection of papers that were presented at the School in Ergodic Theory, CIRM (Marseille, France) during April 2006, explores several themes. Dynamical properties of interval maps are studied in case of unimodal transformations and piecewise monotonic maps, but also for generalized \(\beta\)shift and some Gibbs properties related to the Erdös measure, linked to the Golden Number, are investigated. In geometry, combinatorial and ergodic properties of geodesic flows are studied through a coding of such a flow on an hyperbolic surface, and an original approach of the unique ergodicity property of the directional flow on a surface translation (KMS theorem) is provided. Rank one, mixing, selfjoining transformation, and some rigidity properties, are the subject of three papers. For symbolic dynamics, low complexity is represented by the introduction of generalized Toeplitz sequences, and high disorder is involved in searching properties of measures both invariant under the shift and some cellular automata.} A publication of the Société Mathématique de France, Marseilles (SMF), distributed by the AMS in the U.S., Canada, and Mexico. Orders from other countries should be sent to the SMF. Members of the SMF receive a 30% discount from list. Readership Graduate students and research mathematicians interested in number theory. Table of Contents  R. Abe  The cross section map for geodesic flows related to the Hecke and Picard groups
 H. Bruin  Combinatorics of Fibonaccilike unimodal maps
 J. Buzzi  Entropy theory on the interval
 K. Dajani and C. Kalle  A note on the Greedy \(\beta\)transformation with arbitrary digits
 E. H. El Abdalaoui, M. El Machkouri, and A. Nogueira  A criterion of weak mixing property
 S. Gouëzel and E. Lanneau  Un théorème de Kerchkoff, Masur et Smillie: unique ergodicité sur les surfaces plates
 F. Krieger  Toeplitz subshifts and odometers for residually finite groups
 E. Olivier and A. Thomas  Infinite convolution of Bernoulli measures, PV numbers and related problems in the dynamics of fractal geometry
 V. V. Ryzhikov  Selfjoinings of rankone actions and applications
 M. Sablik  Recherche de mesures invariantes pour l'action conjointe d'un automate cellulaire et du décalage
 A. I. Danilenko  Uncountable collection of mixing rankone actions for locally normal groups
