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Problèmes de plongements en géométrie symplectique
No full textThis document concerns the rigidity/flexibility phenomena related to symplectic embeddings, and their applications in symplectic topology. The two main themes developped here are the equidimensionnal symplectic embeddings in dimension 4 and the C^0 symplectic geometry.Ce mémoire concerne les phénomènes de rigidité/flexibilité liés aux plongements et leurs applications en topologie symplectique. Les deux grands thèmes abordés sont les plongements symplectiques équidimensionnels en dimension 4 et la géometrie symplectique C^0
Dynamique des applications holomorphes propres de domaines reguliers et probleme de l'injectivite
No full text25 pages, 3 figuresThis paper deals with proper holomorphic self-maps of smoothly bounded pseudoconvex domains in \C^2. We study the dynamical properties of their extension to the boundary and show that their non-wandering sets are always contained in the weakly pseudoconvex part of the boundary. In the case of complete circular domains, we combine this fact with an entropy/degree argument to show that the maps are automorphisms. Some of our results remain true in \C^n
Algebraic singularities and symplectic domains
No full textL’objectif de cette thèse est d’approfondir les liens mis en lumière par McDuff-Polterovic, Biran et Opshtein entre l’existence de plongements de domaines symplectiques dans une variété symplectique et l’existence de courbes symplectiques réalisant des singularités algébriques planes isolées dans ces variétés. Pour ce faire, on rappelle dans un premier temps des notions essentielles de géométrie symplectique : courbes J-holomorphes, inflations, et des techniques algébriques : résolution de singularité algébrique. Dans un second temps on explique comment construire un analogue symplectique de la résolution algébrique permettant de construire une forme symplectique sur un éclatement algébrique et comment itérer ce procédé afin de résoudre une singularité algébrique réalisée par une courbe symplectique de sorte que le diviseur exceptionnel soit symplectique à croisements normaux et tel que la courbe résolu soit symplectique. Dans une troisième partie on explique comment construire un domaine symplectique associé à un diviseur exceptionnel à l’aide d’un analogue symplectique de la contraction algébrique et on donne leurs propriétés. Dans une quatrième partie on démontre les résultats principaux de la thèse. Enfin, on donne quelques exemples de correspondances domaines-singularités et on montre notamment que tout domaine torique concave peut-être associé à une singularité plane et on exhibe un domaine qui semble ne pas en être un.The aim of this thesis is to deepen the links highighted by McDuff-Polterovic, Biran and Opshtein between the existence of the symplectic embedding of a domain into a symplectic manifold and the existence of symplectic curves realizing isolated planar algebraic singularity in such a manifold. For this, we first recall some essentials notions of symplectic geometry, such as J-holomorphic curves and inflation technics, and the technic of algebraic resolution of singularities. Secondly, we explain how to build symplectic analogue of algebraic resolution that allows us to endow a complexe blow-up with a symplectic form such that the exceptional divisor is symplectic with normal crossings and such that the resolved curve is also symplectic. In a third part, we explain how the symplectic analogue of the algebraic blow-down allows us to build a symplectic domain associated to the exceptional divisor and we give its properties. In the fourth part, we prove the main theorems of the thesis. Finally, we give some example of correspondence between singularities and domains and we show in particular that any concave toric domain can be associated with a planar algebraic singularity and we exhibit a domain that may not be a concave toric domain
Going Beyond Counting First Authors in Author Co-citation Analysis
Get PDFThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Variations on the Author
Get PDF“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
Appropriate Similarity Measures for Author Cocitation Analysis
Get PDFWe provide a number of new insights into the methodological discussion about author cocitation analysis. We first argue that the use of the Pearson correlation for measuring the similarity between authors’ cocitation profiles is not very satisfactory. We then discuss what kind of similarity measures may be used as an alternative to the Pearson correlation. We consider three similarity measures in particular. One is the well-known cosine. The other two similarity measures have not been used before in the bibliometric literature. Finally, we show by means of an example that our findings have a high practical relevance.information science;Pearson correlation;cosine;similarity measure;author cocitation analysis
Some quantitative results in C0 symplectic geometry
No full textInternational audienceThis paper proceeds with the study of the C 0-symplectic geometry of smooth submanifolds, as initiated in [Ops09, HLS15], with the main focus on the behaviour of symplectic homeomorphisms with respect to numerical invariants like capacities. Our main result is that a symplectic homeomorphism may preserve and squeeze codimension 4 symplectic submanifolds (C 0-flexibility), while this is impossible for codimension 2 symplectic submanifolds (C 0-rigidity). We also discuss C 0-invariants of coistropic and Lagrangian submanifolds, proving some rigidity results and formulating some conjectures. We finally formulate an Eliashberg-Gromov C 0-rigidity type question for submanifolds, which we solve in many cases. Our main technical tool is a quantitative h-principle result in symplectic geometry
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