Measures and dynamics on Noetherian spaces

We give an explicit description of all finite Borel measures on Noetherian topological spaces X, and characterize them as objects dual to a space of functions on X. We use these results to study the asymptotic behavior of continuous dynamical systems on Noetherian spaces.Comment: Minor revisions, results remain the same. To appear in the Journal of Geometric Analysi

On the growth of local intersection multiplicities in holomorphic dynamics: a conjecture of Arnold

We show by explicit example that local intersection multiplicities in holomorphic dynamical systems can grow arbitrarily fast, answering a question of V. I. Arnold. On the other hand, we provide results showing that such behavior is exceptional, and that typically local intersection multiplicities grow subexponentially.Comment: 13 pages. In version 2, we've included an alternate, more geometric construction of the counterexample to Arnold's conjecture. We've also added new theorems illustrating that Arnold's conjecture holds "generically." To appear in Math. Res. Let

Equidistribution of preimages over nonarchimedean fields for maps of good reduction

In this article we prove an analogue of the equidistribution of preimages theorem from complex dynamics for maps of good reduction over nonarchimedean fields. While in general our result is only a partial analogue of the complex equidistribution theorem, for most maps of good reduction it is a complete analogue. In the particular case when the nonarchimedean field in question is equipped with the trivial absolute value, we are able to supply a strengthening of the theorem, namely that the preimages of any tame valuation equidistribute to a canonical measure.Comment: New version includes a proof that generic endomorphisms of projective space have empty exceptional set. Otherwise minor revisions. To appear in Ann. Inst. Fourie

Growth of attraction rates for iterates of a superattracting germ in dimension two

We study the sequence of attraction rates of iterates of a dominant superattracting holomorphic fixed point germ f:(C^2,0)->(C^2,0). By using valuative techniques similar to those developed by Favre-Jonsson, we show that this sequence eventually satisfies an integral linear recursion relation, which, up to replacing f by an iterate, can be taken to have order at most two. In addition, when the germ f is finite, we show the existence of a bimeromorphic model of (C^2,0) where f satisfies a weak local algebraic stability condition.Comment: 27 pages, 1 figur

Charismes pauliniens et charisme wébérien, des « faux-amis » ?

Weber a emprunté le mot charisme à Paul, puis son concept d’autorité charismatique a influencé la manière dont on lisait Paul. Or, il appert que l’on a affaire à un phénomène de « faux-amis » entre la langue théologique et la langue sociologique. En Rm 12, 1 Co 12—14 et Ep 4, les charismes désignent les dons de Dieu, multiples et différenciés, distribués en vue de la construction de la communauté. Ils ne sont pas à comprendre chez Paul tant en termes de leadership ou de pouvoir monologique, qu’en termes de fonctionnement organique, puisqu’il est question de la circulation d’une parole multiple qui débouche sur l’action. Par ailleurs, si l’idéaltype wébérien du charisme prophétique peut éclairer en partie le fonctionnement du charisme paulinien d’apôtre, le concept de charisme spécifique permet de mieux rendre compte du fonctionnement de l’ensemble des charismes pauliniens.Weber borrowed the word charisma from Paul, then his concept of charismatic authority had its own impact on Pauline studies. This is a “false-friends” vocabulary case between theological and sociological languages. In Rom 12, 1 Cor 12-14 and Eph 4, charismas appear to be God’s gifts — numerous, various and distributed for the building of the community. One should understand Pauline charisma not so much in terms of leadership or power, than in terms of an organic functioning : the circulation of speech between many voices, with concrete action as a result. Besides, if the Weberian idealtype of prophetic charisma could partially explain the apostolic charisma, then the concept of specific charisma describes better, altogether, the other charismas

Caïn, protégé du Seigneur ? Les voix de Gn 4,1-16 dans une perspective narratologique

La Bible interdit de représenter Dieu « en image » mais ne se prive pas de le mettre en scène dans des récits. Comment alors éviter que le lecteur ne se fabrique une « image de Dieu narrative » idolâtre ? À partir du récit de Caïn et Abel (Gn 4), analysé sous l’angle des dialogues et des points de vue différenciés des personnages, l’article démontre que la narration biblique, par la manière dont elle raconte, brouille la représentation de Dieu et invite à une lecture dialogique. Loin de la lecture moralisante et culpabilisante traditionnelle (qui reprend uniquement le point de vue de Caïn), on se rend compte que le récit insiste sur les multiples initiatives divines pour entrer en discussion avec Caïn afin de le faire advenir réellement à lui-même, comme individu moralement responsable. En introduction, une réflexion est proposée quant à l’intérêt de la narratologie pour évaluer le jeu des multiples relectures artistiques d’un récit biblique et pour établir un dialogue interdisciplinaire entre l’exégèse et l’histoire de l’art.The Bible forbids any human made representation of God in the form of an image but it does present him as an actor in the narratives. How then can we avoid the fact that the reader can make for him/herself an idolatrous image of God ? This article analyses the story of Cain and Abel (Gen 4) from the point of view of the dialogues and of the different viewpoints of the actors. It shows that be biblical narrative muddles up the representation of God and thus paves the way for a dialogical reading. Far from the traditional reading which interprets the text in a moral way while inducing a guilt feeling (which only takes into account Cain’s point of view), it can be seen that the narrative insists on the multiple initiatives of God in order to create a dialogue with Cain so that he may become really himself, as an morally responsible individual. The introduction proposes a reflection on the interest of narratology to evaluate the reading of the multiple artistic interpretations of a biblical narrative and to establish an interdisciplinary dialogue between exegesis and the history of art