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

Zeta functions and Dynamical Systems

In this brief note we present a very simple strategy to investigate dynamical determinants for uniformly hyperbolic systems. The construction builds on the recent introduction of suitable functional spaces which allow to transform simple heuristic arguments in rigorous ones. Although the results so obtained are not exactly optimal the straightforwardness of the argument makes it noticeable.Comment: 7 pages, no figuer

Linear response formula for piecewise expanding unimodal maps

The average R(t) of a smooth function with respect to the SRB measure of a smooth one-parameter family f_t of piecewise expanding interval maps is not always Lipschitz. We prove that if f_t is tangent to the topological class of f_0, then R(t) is differentiable at zero, and the derivative coincides with the resummation previously proposed by the first named author of the (a priori divergent) series given by Ruelle's conjecture.Comment: We added Theorem 7.1 which shows that the horizontality condition is necessary. The paper "Smooth deformations..." containing Thm 2.8 is now available on the arxiv; see also Corrigendum arXiv:1205.5468 (to appear Nonlinearity 2012

Dissipation time and decay of correlations

We consider the effect of noise on the dynamics generated by volume-preserving maps on a d-dimensional torus. The quantity we use to measure the irreversibility of the dynamics is the dissipation time. We focus on the asymptotic behaviour of this time in the limit of small noise. We derive universal lower and upper bounds for the dissipation time in terms of various properties of the map and its associated propagators: spectral properties, local expansivity, and global mixing properties. We show that the dissipation is slow for a general class of non-weakly-mixing maps; on the opposite, it is fast for a large class of exponentially mixing systems which include uniformly expanding maps and Anosov diffeomorphisms.Comment: 26 Pages, LaTex. Submitted to Nonlinearit

On the susceptibility function of piecewise expanding interval maps

We study the susceptibility function Psi(z) associated to the perturbation f_t=f+tX of a piecewise expanding interval map f. The analysis is based on a spectral description of transfer operators. It gives in particular sufficient conditions which guarantee that Psi(z) is holomorphic in a disc of larger than one. Although Psi(1) is the formal derivative of the SRB measure of f_t with respect to t, we present examples satisfying our conditions so that the SRB measure is not Lipschitz.*We propose a new version of Ruelle's conjectures.* In v2, we corrected a few minor mistakes and added Conjectures A-B and Remark 4.5. In v3, we corrected the perturbation (X(f(x)) instead of X(x)), in particular in the examples from Section 6. As a consequence, Psi(z) has a pole at z=1 for these examples.Comment: To appear Comm. Math. Phy

Mapping the Research Productivity of Three Medical Sciences Journals Published in Saudi Arabia: A Comparative Bibliometric Study

Introduction: The purpose of this study was to compare the progress of research outcomes specifically of three old and new established Saudi medical research journals: Saudi Journal of Medicine and Medical Sciences (SJMMS), Journal of Saudi Heart Association (JSHA), and Journal of Infection and Public Health (JIPH) for the period of 2013 to 2017. Materials and Methods: Scientific papers under the titles of original and review articles, short communications, case and short reports were downloaded from the websites of these journals. The data was analyzed according to three parameters: the growth of publication, the types of publication, and the authorship pattern. Results: The findings of the study revealed that 827 articles were contributed by 3808 authors with an average of 4.6 authors per article, and 12.9% articles were published in 64 issues of SJMMS (n=600, 15.7%) , JSHA (n=951, 24.9%), and JIPH (n=2257, 59.2%) during 2013–2017. The majority of articles (n=746, 90.2%) included more than one author, leaving only 81 articles (9.7%) were prepared by single (or solo) authors. The authors have been collaborated with national and international authors for their scholarly work. Conclusions: The comparison of bibliometric indicators of the three medical journals showed the rising tendency of research publications and the high rate of collaborative research output. These journals contributed a massive number of research papers during the period of five years. Collaboration among researchers facilitates sharing knowledge and techniques and brings a mixture of positive scientific thoughts. The unified bylaws for faculty in Saudi universities should give more weight to multi-authored papers

Three Cationic: Nonporous CuI-Coordination Polymers: Structural Investigation and Vapor Iodine Capture

Three cationic nonporous copper(I) coordination polymers containing bis-pyrazolyl flexible ligands have been prepared and characterized, namely, [Cu(\u3bc-bdb)1.5](PF6)n (1), [Cu(\u3bc-bpb)2](PF6)n (2), and [Cu(\u3bc-bpmb)2](PF6)n (3) (bdb = 1,4-bis(3,5-dimethylpyrazolyl) methyl)benzene; bpb = 1,4-bis(pyrazolyl)butane; bpmb = 1,4-bis(pyrazolyl)methyl)benzene). All compounds were characterized by infrared, powder X-ray diffraction, elemental and thermal analyses, and single-crystal X-ray diffraction. Compound 1, with methyl-substituted pyrazolyl ligand, forms a chain of alternating rings and ribbons in which the copper(I) centers are three coordinated in distorted trigonal planar geometry. In compounds 2 and 3 copper(I) atoms adopt distorted tetrahedral geometries giving two-dimensional sheet structures with 44-sql topology. Interestingly, iodine sorption experiments show that colorless crystals of 2 and 3 remain unchanged in the presence of iodine vapors, while the three-coordinated compound 1 immediately absorbs iodine and turns dark. Anion exchange behavior of compounds 1 and 2 was also investigated both in solution and in the solid state

Convergence of invariant densities in the small-noise limit

This paper presents a systematic numerical study of the effects of noise on the invariant probability densities of dynamical systems with varying degrees of hyperbolicity. It is found that the rate of convergence of invariant densities in the small-noise limit is frequently governed by power laws. In addition, a simple heuristic is proposed and found to correctly predict the power law exponent in exponentially mixing systems. In systems which are not exponentially mixing, the heuristic provides only an upper bound on the power law exponent. As this numerical study requires the computation of invariant densities across more than 2 decades of noise amplitudes, it also provides an opportunity to discuss and compare standard numerical methods for computing invariant probability densities.Comment: 27 pages, 19 figures, revised with minor correction

Effects of the Bacterial Extract OM-85 on Phagocyte Functions and the Stress Response

The effects of the bacterial extract OM-85 on the respiratory burst, intracellular calcium and the stress response have been investigated in human peripheral blood monocytes from normal donors. Activation of the respiratory burst during bacterial phagocytosis has been previously associated with heat shock/stress proteins synthesis. Whereas OM-85 stimulated superoxide production and increased Ca2+ mobilization, it fared to induce synthesis of classical HSPs. The lack of stress protein induction was observed even in the presence of iron which potentiates both oxidative injury and stress protein induction during bacterial phagocytosis. However OM-85 induced a 75–78 kDa protein, which is likely to be a glucose regulated protein (GRP78), and enhanced intracellular expression of interleukin-lβ precursor

Rare events, escape rates and quasistationarity: some exact formulae

We present a common framework to study decay and exchanges rates in a wide class of dynamical systems. Several applications, ranging form the metric theory of continuons fractions and the Shannon capacity of contrained systems to the decay rate of metastable states, are given