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École de Théorie Ergodique (2006)
Edited by: Y. Lacroix, Université du Sud-Toulon-Var SITV, La Valette du Var, France, P. Liardet, Université de Provence, Marseille, France, and J. -P. Thouvenot, Université Pierre et Marie Curie, Paris, France
A publication of the Société Mathématique de France.
Séminaires et Congrès
2011; 251 pp; softcover
Number: 20
ISBN-10: 2-85629-312-3
ISBN-13: 978-2-85629-312-6
List Price: US$60
Member Price: US$48
Order Code: SECO/20
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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, self-joining 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.


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 Fibonacci-like 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 -- Self-joinings of rank-one 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 rank-one actions for locally normal groups
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