89 research outputs found
Fatou maps in dynamics
No full textWe study the dynamics of a holomorphic self-map f of complexprojective space of degree d>1 by utilizing the notion of aFatou map, introduced originally by Ueda (1997) and independentlyby the author (2000). A Fatou map is intuitively like an analyticsubvariety on which the dynamics of f are a normal family (such as a local stable manifold of a hyperbolic periodic point). We show that global stable manifolds of hyperbolic fixed points are given by Fatou maps. We further show that they are necessarily Kobayashi hyperbolic and are always ramified by f (and therefore any hyperbolic periodic point attracts a point of thecritical set of f). We also show that Fatou components arehyperbolically embedded in ℙn and that a Fatou component which is attracted to a taut subset of itself isnecessarily taut.Peer Reviewe
Hyperbolic entire functions with bounded Fatou components
No full textAgraïments: The third author was supported by a Philip Leverhulme Prize.We show that an invariant Fatou component of a hyperbolic transcendental entire function is a Jordan domain (in fact, a quasidisc) if and only if it contains only finitely many critical points and no asymptotic curves. We use this theorem to prove criteria for the boundedness of Fatou components and local connectivity of Julia sets for hyperbolic entire functions, and give examples that demonstrate that our results are optimal. A particularly strong dichotomy is obtained in the case of a function with precisely two critical values
Introduction to Fatou components in holomorphic dynamics
No full textThis work is part of the C.I.M.E. Lecture Notes ``Modern Aspects of Dynamical Systems'' to be published in the Springer Lecture Notes in Mathematics -- C.I.M.E. subseries, corresponding to the course taught by the second author in Cetraro in August 2021.This survey is an introduction to the classification of Fatou components in holomorphic dynamics. We start with the description of the Fatou and Julia sets for rational maps of the Riemann sphere, and finish with an updated account of the recent results on Fatou components for polynomial skew-products in complex dimension two, where we focus on the key steps in the construction giving the existence of a wandering domain for a polynomial endomorphism of
Fatou and brothers Riesz theorems in the infinite-dimensional polydisc
No full textWe study the boundary behavior of functions in the Hardy spaces on the infinite-dimensional polydisc. These spaces are intimately related to the Hardy spaces of Dirichlet series. We exhibit several Fatou and Marcinkiewicz- Zygmund type theorems for radial convergence of functions with Fourier spectrum supported on N0∞∪(−N0∞). As a consequence one obtains easy new proofs of the brothers F. and M. Riesz Theorems in infinite dimensions, as well as being able to extend a result of Rudin concerning which functions are equal to the modulus of an H 1 function almost everywhere to T ∞ . Finally, we provide counterexamples showing that the pointwise Fatou theorem is not true in infinite dimensions without restrictions to the mode of radial convergence even for bounded analytic functions
The uncapturable contours of an author : Ambiguous postures in French media of transnational Francophone writers Fatou Diome and Alain Mabanckou
No full textThe Francophone authors Fatou Diome (Senegalese origins) and Alain Mabanckou (Congolese origins) are at the centre of this study on author postures in audio-visual media. The purpose of the study is to determine how transnational authors position themselves inside a central dominating culture and language, in this case France and French. Eight media samples for each author have been collected on Internet. The selection of the material was based on the most recent examples, a variety of modality-rich French media contexts, a representative view of the authorships and moments where identity positionings were activated. The theoretical framing leans on anterior results related to the circulation and reception of Francophone authors in Scandinavia and Sweden. Previous findings point Francophone authors as categorized through dichotomies, such as exotic-authentic, nationaltransnational and local-global. These oppositional terms have been used as analytical tools in the analysis of the data samples, in order to uncover how the author relates to these categories, takes advantage of them, and/or breaks with them in their construction of an author posture. The results show that Diome and Mabanckou adopt conscious strategies in order to avoid definitions, as well as to renegotiate concepts, such as ‘national’ and ‘migrant’. Mabanckou’s and Diome’s appearances in the media sample shed light on how transnational authors cultivate a posture in movement, and develop strategies of ‘reversibility’, ‘renegotiation’, ‘rebellion’, and ‘transgression of borders’.</p
The uncapturable contours of an author: Ambiguous postures in French media of transnational Francophone writers Fatou Diome and Alain Mabanckou
No full textThe Francophone authors Fatou Diome (Senegalese origins) and Alain Mabanckou (Congolese origins) are at the centre of this study on author postures in audio-visual media. The purpose of the study is to determine how transnational authors position themselves inside a central dominating culture and language, in this case France and French. Eight media samples for each author have been collected on Internet. The selection of the material was based on the most recent examples, a variety of modality-rich French media contexts, a representative view of the authorships and moments where identity positionings were activated. The theoretical framing leans on anterior results related to the circulation and reception of Francophone authors in Scandinavia and Sweden. Previous findings point Francophone authors as categorized through dichotomies, such as exotic-authentic, national-transnational and local-global. These oppositional terms have been used as analytical tools in the analysis of the data samples, in order to uncover how the author relates to these categories, takes advantage of them, and/or breaks with them in their construction of an author posture. The results show that Diome and Mabanckou adopt conscious strategies in order to avoid definitions, as well as to renegotiate concepts, such as ‘national’ and ‘migrant’. Mabanckou’s and Diome’s appearances in the media sample shed light on how transnational authors cultivate a posture in movement, and develop strategies of ‘reversibility’, ‘renegotiation’, ‘rebellion’, and ‘transgression of borders’
Ethè discursifs africains au bord de la Seine. L’exemple de Fatou Diome
No full textThe analysis of enounciative subjectivity in Fatou Diome’s works allows us to focus on the contemporary French-Parisian literary landscape, and on the strategies of locating African writers, or of African descent, within the field. The use of stereotypes about the African writer, and of the exotic discourse emanating from the doxa, reveal that contemporary authors are forced to develop discursive and media strategies to negotiate a place of legitimacy in the French literary field that overlaps partly with the Francophone and worldwide field, but whose objectives and the public reception are not always shared. Fatou Diome’s case study enables discursive analysis on rhetorical ethè, and on how she manages the fictional and mediatical “I”. But it also sheds light on the use of “us” in her pamphlet Marianne porte plainte! that may refer to different communities. The identification of effective positions taken on by the author will then enable us to appreciate the potential for transformation with regard to the consecration and canonisation processes governed by the “center” institutions. The “African” character attributed to both authors and literary productions is the main issue. It remains to be seen whether and how writers who claim literary autonomy are willing to play the “difference” card to satisfy the public who is structurally close to the dominant discourse.The analysis of enounciative subjectivity in Fatou Diome’s works allows us to focus on the contemporary French-Parisian literary landscape, and on the strategies of locating African writers, or of African descent, within the field. The use of stereotypes about the African writer, and of the exotic discourse emanating from the doxa, reveal that contemporary authors are forced to develop discursive and media strategies to negotiate a place of legitimacy in the French literary field that overlaps partly with the Francophone and worldwide field, but whose objectives and the public reception are not always shared. Fatou Diome’s case study enables discursive analysis on rhetorical ethè, and on how she manages the fictional and mediatical “I”. But it also sheds light on the use of “us” in her pamphlet Marianne porte plainte! that may refer to different communities. The identification of effective positions taken on by the author will then enable us to appreciate the potential for transformation with regard to the consecration and canonisation processes governed by the “center” institutions. The “African” character attributed to both authors and literary productions is the main issue. It remains to be seen whether and how writers who claim literary autonomy are willing to play the “difference” card to satisfy the public who is structurally close to the dominant discourse
Mesure du quatrième cumulant du bruit photo-assisté dans une jonction tunnel en régime classique.
No full textLes statistiques des fluctuations de courant dans un échantillon mésoscopique sous irradiation n'ont jamais été explorées au-delà de la variance et du troisième moment. Nous rapportons la première mesure du quatrième cumulant de bruit dans une jonction tunnel dans le régime classique (c'est-à-dire k [indice inférieur B]T >> h f) en présence d'un courant continu et d'une excitation micro-onde en utilisant deux méthodes. Tout d'abord, nous avons étudié la corrélation entre les fluctuations de puissance à deux fréquences, f [indice inférieur 1] = 4,5 GHz et f [indice inférieur 2] = 7,15 GHz. Cette corrélation existe seulement pour certaines fréquences d'excitation.
Nous avons également effectué une mesure directe des statistiques en numérisant le bruit à grande vitesse après conversion vers les basses fréquences. Les résultats obtenus à partir de ces expériences sont en très bon accord avec les prédictions théoriques de la dynamique de bruit. En terme de photons, le quatrième cumulant correspond à une corrélation entre les photons de différentes fréquences.
-- The statistics of current fluctuations in a mesoscopic sample under irradiation has never been explored beyond the variance and third moment. We report the first measurement of the fourth cumulant of noise in a tunnel junction in the classical regime (i.e. k[subscript B] T >> hf) in the presence of a d.c and microwave excitation, using two methods. First, we have investigated the correlation between the power fluctuations at two frequencies, f[subscript 1] = 4.5 GHz and f[subscript 2] = 7.15 GHz. This correlation exists only for certain excitation frequencies. We have also performed a direct measurement of the statistics by digitizing the noise at high speed after down conversion. The results obtained from these experiments are in very good agreement with the theoretical predictions of noise dynamics. In terms of photons, the fourth cumulant corresponds to a correlation between photons of different frequencies
Mesure du quatrième cumulant du bruit photo-assisté dans une jonction tunnel en régime classique.
No full textLes statistiques des fluctuations de courant dans un échantillon mésoscopique sous irradiation n'ont jamais été explorées au-delà de la variance et du troisième moment. Nous rapportons la première mesure du quatrième cumulant de bruit dans une jonction tunnel dans le régime classique (c'est-à-dire k [indice inférieur B]T >> h f) en présence d'un courant continu et d'une excitation micro-onde en utilisant deux méthodes. Tout d'abord, nous avons étudié la corrélation entre les fluctuations de puissance à deux fréquences, f [indice inférieur 1] = 4,5 GHz et f [indice inférieur 2] = 7,15 GHz. Cette corrélation existe seulement pour certaines fréquences d'excitation.
Nous avons également effectué une mesure directe des statistiques en numérisant le bruit à grande vitesse après conversion vers les basses fréquences. Les résultats obtenus à partir de ces expériences sont en très bon accord avec les prédictions théoriques de la dynamique de bruit. En terme de photons, le quatrième cumulant correspond à une corrélation entre les photons de différentes fréquences.
-- The statistics of current fluctuations in a mesoscopic sample under irradiation has never been explored beyond the variance and third moment. We report the first measurement of the fourth cumulant of noise in a tunnel junction in the classical regime (i.e. k[subscript B] T >> hf) in the presence of a d.c and microwave excitation, using two methods. First, we have investigated the correlation between the power fluctuations at two frequencies, f[subscript 1] = 4.5 GHz and f[subscript 2] = 7.15 GHz. This correlation exists only for certain excitation frequencies. We have also performed a direct measurement of the statistics by digitizing the noise at high speed after down conversion. The results obtained from these experiments are in very good agreement with the theoretical predictions of noise dynamics. In terms of photons, the fourth cumulant corresponds to a correlation between photons of different frequencies
Les noms et les titres sarcastiques dans une traduction anglaise de La Préférence Nationale de Fatou Diome
No full textCe mémoire se propose d’étudier le sarcasme: son usage, son lien fort avec la culture et sa traduisibilité. En traduisant La Préférence Nationale de Fatou Diome, nous examinons la difficulté de transmettre le sarcasme sous-entendu dans les noms et dans les titres de ce livre. Le traducteur comme médiateur linguistique et culturel doit jauger l’importance des éléments qui entrent en jeu pendant l’acte traduisant. Comme cette traduction anglaise nous le démontre, le traducteur doit souvent prendre la décision soit d’amener son lectorat vers l’écrivain soit d’amener l’écrivain vers son lectorat- un choix qui, entre autres, pourrait mettre en question la fidélité du traducteur.
This thesis proposes to study sarcasm: its use, its strong link to culture and its translatability. By translating Fatou Diome’s La Préférence Nationale, we examine the difficulty in conveying the implicit sarcasm in the names and the titles of this book. As both a linguistic and cultural intermediary, the translator has to gauge the importance of the elements that come into play during the translation process. As this English translation attempts to show, the translator must often make the decision to either steer his or her readership towards the author or to steer the author towards his or her readership- a choice that, amongst other things, might call into question the faithfulness of the translator.Includes bibliographical references (pages 24-27)
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