Equilibrium states for non-uniformly expanding maps: decay of correlations and strong stability

We study the rate of decay of correlations for equilibrium states associated to a robust class of non-uniformly expanding maps where no Markov assumption is required. We show that the Ruelle-Perron-Frobenius operator acting on the space of Holder continuous observables has a spectral gap and deduce the exponential decay of correlations and the central limit theorem. In particular, we obtain an alternative proof for the existence and uniqueness of the equilibrium states and we prove that the topological pressure varies continuously. Finally, we use the spectral properties of the transfer operators in space of differentiable observables to obtain strong stability results under deterministic and random perturbations.Comment: 29 pages, Annales de l'Institut Henri Poincare - Analyse non lineaire (to appear

Entropic Fluctuations in Statistical Mechanics I. Classical Dynamical Systems

Within the abstract framework of dynamical system theory we describe a general approach to the Transient (or Evans-Searles) and Steady State (or Gallavotti-Cohen) Fluctuation Theorems of non-equilibrium statistical mechanics. Our main objective is to display the minimal, model independent mathematical structure at work behind fluctuation theorems. Besides its conceptual simplicity, another advantage of our approach is its natural extension to quantum statistical mechanics which will be presented in a companion paper. We shall discuss several examples including thermostated systems, open Hamiltonian systems, chaotic homeomorphisms of compact metric spaces and Anosov diffeomorphisms.Comment: 72 pages, revised version 12/10/2010, to be published in Nonlinearit

Amenability of groups and GG-sets

This text surveys classical and recent results in the field of amenability of groups, from a combinatorial standpoint. It has served as the support of courses at the University of G\"ottingen and the \'Ecole Normale Sup\'erieure. The goals of the text are (1) to be as self-contained as possible, so as to serve as a good introduction for newcomers to the field; (2) to stress the use of combinatorial tools, in collaboration with functional analysis, probability etc., with discrete groups in focus; (3) to consider from the beginning the more general notion of amenable actions; (4) to describe recent classes of examples, and in particular groups acting on Cantor sets and topological full groups

Risques sanitaires liés aux radiations. Radioprotection.

National audienc

Surgical Staff Radiation Protection During Fluoroscopy-Guided Urologic Interventions

International audienceINTRODUCTION: Over the past 20 years, the use of fluoroscopy to guide urologic surgical interventions has been constantly growing. Thus, in their daily practice, urologists and other operating room (OR) staff are exposed to X-radiation increasingly frequently. This raises questions as to the risks they encounter and the actions needed to reduce them. OBJECTIVE: Evaluate X-ray dose exposure in the members of the surgical team and determine urologist radioprotection knowledge and practices. MATERIALS AND METHODS: A prospective bicenter study was conducted within AFUF (French urology resident association) and in association with The French Nuclear Safety Authority/The Institute for Radiological Protection and Nuclear Safety (ASN/IRSN). Radiation exposure was measured on 12 operators using dosimeters (seven per operator), in staff-occupied locations in the OR using ionization chambers, and on anthropomorphic phantoms. A survey was used to gather information on radiation knowledge and safety practices of the AFUF members. RESULTS: Annual whole-body radiation doses were low (0.1-0.8 millisieverts [mSv], mostly at around 0.3 mSv), and equivalent doses were low for the fingers (0.7-15 mSv, mostly at around 2.5 mSv), and low for the lens of the eye (0.3-2.3 mSv, mostly at around 0.7 mSv). In percutaneous nephrolithotomy, extremity doses were lower when the patient was placed in dorsal decubitus compared with ventral decubitus. Pulsed fluoroscopy reduced radiation dose exposure by a factor of 3 compared with continuous fluoroscopy with no image quality loss. Radiation safety practices were poor: only 15% of urologists wore dosimeters and only 5% had been trained in the handling of X-ray generators. CONCLUSION: In the present study, radiation exposure for urologists was low, but so was knowledge of radiation safety and optimization practices. This absence of training for radiation safety and reduction, teamed with novel techniques involving long fluoroscopy-guided interventions, could result in unnecessarily high exposure for patients and OR personne