Conformal measures for multidimensional piecewise invertible maps

Given a piecewise invertible map T:X\to X and a weight g:X\rightarrow\ ]0,\infty[ , a conformal measure \nu is a probability measure on X such that, for all measurable A\subset X with T:A\to TA invertible, \nu(TA)= \lambda \int_{A}\frac{1}{g}\ d\nu with a constant \lambda>0 . Such a measure is an essential tool for the study of equilibrium states. Assuming that the topological pressure of the boundary is small, that \log g has bounded distortion and an irreducibility condition, we build such a conformal measure.

Inflight Radiometric Calibration of New Horizons' Multispectral Visible Imaging Camera (MVIC)

© 2016 Elsevier Inc. We discuss two semi-independent calibration techniques used to determine the inflight radiometric calibration for the New Horizons’ Multi-spectral Visible Imaging Camera (MVIC). The first calibration technique compares the measured number of counts (DN) observed from a number of well calibrated stars to those predicted using the component-level calibration. The ratio of these values provides a multiplicative factor that allows a conversation between the preflight calibration to the more accurate inflight one, for each detector. The second calibration technique is a channel-wise relative radiometric calibration for MVIC's blue, near-infrared and methane color channels us…

Produits aléatoires d'opérateurs matrices de transfert

Nous etudions le comportement asymptotique de produits aleatoires d'operateurs de Ruelle-Perron-Frobenius. Nous etendons le travail de Ruelle obtenu dans le cas homogene, au cas aleatoire.

Repetition times for Gibbsian sources

In this paper we consider the class of stochastic stationary sources induced by one-dimensional Gibbs states, with Holder continuous potentials. We show that the time elapsed before the source repeats its first n symbols, when suitably renormalized, converges in law either to a log-normal distribution or to a finite mixture of exponential random variables. In the first case we also prove a large deviation result.

Virtual Atomic and Molecular Data Center

(special issue HighRus2009). VAMDC; International audience

Vitesse de convergence vers l'état d'équilibre pour des dynamiques markoviennes non höldériennes

Resume On etudie la vitesse de convergence vers l'etat d'equilibre pour des dynamiques markoviennes non holderiennes. On obtient une estimation de la vitesse de melange sur un sous-espace B dense dans l'espace des fonctions continues. En outre, on montre que le spectre de l'operateur de Perron-Frobenius, restreint a B , est un disque ferme dont chaque point est une valeur propre. Ceci implique que la vitesse de convergence vers l'etat d'equilibre ne peut pas etre exponentielle.

Effects of dietary conjugated linoleic acids in the control of adiposity and obesity‐related disorders

The body fat-lowering effect of conjugated linoleic acids (CLA) in experimental animals has attracted much interest because of the potential use of CLA as weight loss agents in humans. The objective of this review was to give an overview of the results from human intervention trials. The review also addresses experimental studies in animal models and in cultured cells. CLA appear to provoke fat mass loss and an increase of fat-free mass in rodents, but the results in humans are inconsistent and much less clear than in rodents. Thus, the results of studies in humans do not support a body fat-lowering effect of CLA. There are indications from animal studies that the trans-10, cis-12 CLA isome…

Abnormal escape rates from nonuniformly hyperbolic sets

Consider a $C^{1+\epsilon}$ diffeomorphism $f$ having a uniformly hyperbolic compact invariant set $\Omega$, maximal invariant in some small neighbourhood of itself. The asymptotic exponential rate of escape from any small enough neighbourhood of $\Omega$ is given by the topological pressure of $-\log |J^u f|$ on $\Omega$ (Bowen–Ruelle in 1975). It has been conjectured (Eckmann–Ruelle in 1985) that this property, formulated in terms of escape from the support $\Omega$ of a (generalized Sinai–Ruelle–Bowen (SRB)) measure, using its entropy and positive Lyapunov exponents, holds more generally. We present a simple $C^\infty$ two-dimensional counterexample, constructed by a surgery using a Bowe…

Virtual atomic and molecular data centre

The Virtual Atomic and Molecular Data Centre (VAMDC, http://www.vamdc.eu) is a European Union funded collaboration between groups involved in the generation, evaluation, and use of atomic and molecular data. VAMDC aims to build a secure, documented, flexible and interoperable e-science environment-based interface to existing atomic and molecular data. The project will cover establishing the core consortium, the development and deployment of the infrastructure and the development of interfaces to the existing atomic and molecular databases. It will also provide a forum for training potential users and dissemination of expertise worldwide. This review describes the scope of the VAMDC project;…

The pianigiani-yorke measure for topological markov chains

We prove the existence of a Pianigiani-Yorke measure for a Markovian factor of a topological Markov chain. This measure induces a Gibbs measure in the limit set. The proof uses the contraction properties of the Ruelle-Perron-Frobenius operator.

Titan's surface albedo variations over a Titan season from near-infrared CFHT/FTS spectra

International audience; We have observed Titan in a series of campaigns from 1991 to 1996 with the Fourier Transform Spectrometer on the CFH telescope. The data acquired provide a lightcurve from the geometric albedos in the 0.9–View the MathML source spectral region. The 1991–1993 data were previously analyzed in Coustenis et al. [1995. Titan's surface: composition and variability from its near-infrared albedo. Icarus 118, 87–104] with a spherical particle code by McKay et al. [1989. The thermal structure of Titan's atmosphere. Icarus 80, 23–53]. We present here three new datasets from the 1994, 1995 and 1996 observations, with additional information from the 0.94-μm methane window on Tita…

Titan's 3-micron spectral region from ISO high-resolution spectroscopy

Abstract The near-infrared spectrum of Titan, Saturn's largest moon and one of the Cassini/Huygens' space mission primary targets, covers the 0.8 to 5 micron region in which it shows several weak CH 4 absorption regions, and in particular one centered near 2.75 micron. Due to the interference of telluric absorption, only part of this window region (2.9–3.1 μm) has previously been observed from the ground [Noll, K.S., Geballe, T.R., Knacke, R., Pendleton, F., Yvonne, J., 1996. Icarus 124, 625–631; Griffith, C.A., Owen, T., Miller, G.A., Geballe, T., 1998. Nature 395, 575–578; Griffith, C.A., Owen, T., Geballe, T.R., Rayner, J., Rannou, P., 2003. Science 300, 628–630; Geballe, T.R., Kim, S.J.…

Poincare Inequalities and Spectral Gap, Concentration Phenomenon for G-Measures

We produce a new approach based upon inequalities of Poincare’s type for giving constructive estimates of the mixing rate for a family of mixing stationary processes continuously depending on their past called g-measures. We establish also exponential inequalities of Hoeffding’s type leading to a concentration phenomenon for a large class of observables; this last property permits in particular to give the typical behaviour of the n-orbits of a g-measure.

Invariant measures for piecewise convex transformations of an interval

Devroye Inequality for a Class of Non-Uniformly Hyperbolic Dynamical Systems

In this paper, we prove an inequality, which we call "Devroye inequality", for a large class of non-uniformly hyperbolic dynamical systems (M,f). This class, introduced by L.-S. Young, includes families of piece-wise hyperbolic maps (Lozi-like maps), scattering billiards (e.g., planar Lorentz gas), unimodal and H{\'e}non-like maps. Devroye inequality provides an upper bound for the variance of observables of the form K(x,f(x),...,f^{n-1}(x)), where K is any separately Holder continuous function of n variables. In particular, we can deal with observables which are not Birkhoff averages. We will show in \cite{CCS} some applications of Devroye inequality to statistical properties of this class…

Quasi-Stationary Distribution and Gibbs Measure of Expanding Systems

Let T be an expanding transformation defined on A —(J A{, i= 1being a finite collection of connected open bounded subsets of 2Rn,such that T Acontains strictly Aand Tis Markovian. We prove the existence of a quasi-stationary distrition for T. We show that the T-invariant probability on the limit Cantor set is Gibbsian with potential Log|_DT|. Using the Hilbert projective metric we prove that both distributions are weak limits of conditional laws of probabilities, the speed of convergence being exponential. These results develop a previous work by G. Pianigiani and J.A. Yorke.

On the enhancement of diffusion by chaos, escape rates and stochastic instability

We consider stochastic perturbations of expanding maps of the interval where the noise can project the trajectory outside the interval. We estimate the escape rate as a function of the amplitude of the noise and compare it with the purely diffusive case. This is done under a technical hypothesis which corresponds to stability of the absolutely continuous invariant measure against small perturbations of the map. We also discuss in detail a case of instability and show how stability can be recovered by considering another invariant measure.