Frequent hypercyclicity, chaos, and unconditional Schauder decompositions

We prove that if X is any complex separable infinite-dimensional Banach space with an unconditional Schauder decomposition, X supports an operator T which is chaotic and frequently hypercyclic. This result is extended to complex Frechet spaces with a continuous norm and an unconditional Schauder decomposition, and also to complex Frechet spaces with an unconditional basis, which gives a partial positive answer to a problem posed by Bonet. We also solve a problem of Bes and Chan in the negative by presenting hypercyclic, but non-chaotic operators on \mathbb{C}^\mathbb{N}. We extend the main result to C_0-semigroups of operators. Finally, in contrast with the complex case, we observe that there are real Banach spaces with an unconditional basis which support no chaotic operator.This work was partially supported by ANR-Projet Blanc DYNOP, by the MEC and FEDER Projects MTM2007-64222 and MTM2010-14909, and by Generalitat Valenciana Project PROMETEO/2008/101.De La Rosa Penilla, M.; Frerick, L.; Grivaux, S.; Peris Manguillot, A. (2012). Frequent hypercyclicity, chaos, and unconditional Schauder decompositions. Israel Journal of Mathematics. 190(1):389-399. https://doi.org/10.1007/s11856-011-0210-6S3893991901S. Ansari, Existence of hypercyclic operators on topological vector spaces, Journal of Functional Analysis 148 (1997), 384–390.F. Bayart and S. Grivaux, Frequently hypercyclic operators, Transactions of the American Mathematical Society 358 (2006), 5083–5117.F. Bayart and S. Grivaux, Hypercyclicity and unimodular point spectrum, Journal of Functional Analysis 226 (2005), 281–300.F. Bayart and S. Grivaux, Invariant Gaussian measures for linear operators on Banach spaces and linear dynamics, Proceedings of the London Mathematical Society 94 (2007), 181–210.F. Bayart and É. Matheron, Dynamics of Linear Operators, Cambridge University Press, Cambridge, 2009.L. Bernal-González, On hypercyclic operators on Banach spaces, Proceedings of the American Mathematical Society 127 (1999), 1003–1010.J. Bès and A. Peris, Hereditarily hypercyclic operators, Journal of Functioanl Analysis 167 (1999), 94–112.J. Bonet, F. Martínez-Giménez and A. Peris, A Banach space wich admits no chaotic operator, The Bulletin of the London Mathematical Society 33 (2001), 196–198.M. De la Rosa, L. Frerick, S. Grivaux and A. Peris, Chaos on Fréchet spaces with unconditional basis, preprint.W. T. Gowers, A solution to Banach’s hyperplane problem, The Bulletin of the London Mathematical Society 26 (1994), 523–530.W. T. Gowers and B. Maurey, Banach spaces with small spaces of operators, Mathematische Annalen 307 (1997), 543–568.W. T. Gowers and B. Maurey, The unconditional basic sequence problem, Journal of the American Mathematical Society 6 (1993), 851–874.S. Grivaux, A new class of frequently hypercyclic operators, Indiana University Mathematics Journal, to appear.K. G. Grosse-Erdmann and A. Peris, Linear Chaos, Springer-Verlag, Berlin, 2011.K. B. Laursen and M. M. Neumann, An Introduction to Local Spectral Theory, London Mathematical Society Monographs, New Series, Vol. 20, Clarendon Press, Oxford, 2000.S. Shkarin, On the spectrum of frequently hypercyclic operators, Proceedings of the American Mathematical Society 137 (2009), 123–134

Analysis of 339 pregnancies in 181 women with 13 different forms of inherited thrombocytopenia

65Pregnancy in women with inherited thrombocytopenias is a major matter of concern as both the mothers and the newborns are potentially at risk of bleeding. However, medical management of this condition cannot be based on evidence because of the lack of consistent information in the literature. To advance knowledge on this matter, we performed a multicentric, retrospective study evaluating 339 pregnancies in 181 women with 13 different forms of inherited thrombocytopenia. Neither the degree of thrombocytopenia nor the severity of bleeding tendency worsened during pregnancy and the course of pregnancy did not differ from that of healthy subjects in terms of miscarriages, fetal bleeding and pre-term births. The degree of thrombocytopenia in the babies was similar to that in the mother. Only 7 of 156 affected newborns had delivery-related bleeding, but 2 of them died of cerebral hemorrhage. The frequency of delivery-related maternal bleeding ranged from 6.8% to 14.2% depending on the definition of abnormal blood loss, suggesting that the risk of abnormal blood loss was increased with respect to the general population. However, no mother died or had to undergo hysterectomy to arrest bleeding. The search for parameters predicting delivery-related bleeding in the mother suggested that hemorrhages requiring blood transfusion were more frequent in women with history of severe bleedings before pregnancy and with platelet count at delivery below 50 × 10(9)/L.openopenPatrizia Noris; Nicole Schlegel; Catherine Klersy; Paula G. Heller; Elisa Civaschi; Nuria Pujol-Moix; Fabrizio Fabris; Remi Favier; Paolo Gresele; Véronique Latger-Cannard; Adam Cuker; Paquita Nurden; Andreas Greinacher; Marco Cattaneo; Erica De Candia; Alessandro Pecci; Marie-Françoise Hurtaud-Roux; Ana C. Glembotsky; Eduardo Muñiz-Diaz; Maria Luigia Randi; Nathalie Trillot; Loredana Bury; Thomas Lecompte; Caterina Marconi; Anna Savoia; Carlo L. Balduini; Sophie Bayart; Anne Bauters; Schéhérazade Benabdallah-Guedira; Françoise Boehlen; Jeanne-Yvonne Borg; Roberta Bottega; James Bussel; Daniela De Rocco; Emmanuel de Maistre; Michela Faleschini; Emanuela Falcinelli; Silvia Ferrari; Alina Ferster; Tiziana Fierro; Dominique Fleury; Pierre Fontana; Chloé James; Francois Lanza; Véronique Le Cam Duchez; Giuseppe Loffredo; Pamela Magini; Dominique Martin-Coignard; Fanny Menard; Sandra Mercier; Annamaria Mezzasoma; Pietro Minuz; Ilaria Nichele; Lucia D. Notarangelo; Tommaso Pippucci; Gian Marco Podda; Catherine Pouymayou; Agnes Rigouzzo; Bruno Royer; Pierre Sie; Virginie Siguret; Catherine Trichet; Alessandra Tucci; Béatrice Saposnik; Dino VeneriPatrizia, Noris; Nicole, Schlegel; Catherine, Klersy; Paula G., Heller; Elisa, Civaschi; Nuria Pujol, Moix; Fabrizio, Fabris; Remi, Favier; Paolo, Gresele; Véronique Latger, Cannard; Adam, Cuker; Paquita, Nurden; Andreas, Greinacher; Marco, Cattaneo; Erica De, Candia; Alessandro, Pecci; Marie Françoise Hurtaud, Roux; Ana C., Glembotsky; Eduardo Muñiz, Diaz; Maria Luigia, Randi; Nathalie, Trillot; Loredana, Bury; Thomas, Lecompte; Caterina, Marconi; Savoia, Anna; Carlo L., Balduini; Sophie, Bayart; Anne, Bauters; Schéhérazade Benabdallah, Guedira; Françoise, Boehlen; Jeanne Yvonne, Borg; Bottega, Roberta; James, Bussel; DE ROCCO, Daniela; Emmanuel de, Maistre; Faleschini, Michela; Emanuela, Falcinelli; Silvia, Ferrari; Alina, Ferster; Tiziana, Fierro; Dominique, Fleury; Pierre, Fontana; Chloé, James; Francois, Lanza; Véronique Le Cam, Duchez; Giuseppe, Loffredo; Pamela, Magini; Dominique Martin, Coignard; Fanny, Menard; Sandra, Mercier; Annamaria, Mezzasoma; Pietro, Minuz; Ilaria, Nichele; Lucia D., Notarangelo; Tommaso, Pippucci; Gian Marco, Podda; Catherine, Pouymayou; Agnes, Rigouzzo; Bruno, Royer; Pierre, Sie; Virginie, Siguret; Catherine, Trichet; Alessandra, Tucci; Béatrice, Saposnik; Dino, Vener

Modélisation multi-échelle d un assemblage riveté aéronautique - Vers un modèle de fragilisation structurale

As part of crash simulations, one difficulty concerns the representativeness of material and geometrical non-linear behaviours, especially in the jointed areas. For instance, the mechanical ruin of punched plates is not correctly predicted. ln that sense, the aim of this work is to propose a methodology to formalize and characterize a structural embrittlement model, which will en able to model the structural weakening effects of holes in metallic plates at a macroscopic leve!. The structural embrittlement concept is presented in the first part. Coming from the perforations, the structural embrittlement is defined as the inhomogeneous strain field along the future crack path. The local and nominal strain ratio observed along this crack path enables to measure the embrittlement phenomena. ln the second part, the structural embrittlement mechanisms are analyzed from quasi-static experiments undertaken on punched and not punched samples. The embrittlement model is then formalized and a modelling task is carried out for a better understanding of physical basis of this mode!. The third part is devoted to the development of multiscale tool using a Transformation Field Analysis approach in order to characterize the embrittlement mode!. The elastic developments have shown the feasibility of the method. The plastic behaviour is then implemented in the multiscale model and discussed. Finally, the dependency of the structural model to strain rate is studied using dynamic experiments. Sensitive and insensitive materials are investigated.Dans le cadre de l'étude par éléments finis du crash des structures aéronautiques, la prédiction des modes de ruine engendrés au sein ou au voisinage des assemblages rivetés, telle la déchirure d'une tôle le long d'une ligne de rivets, s'avère, encore aujourd'hui, délicate. Dans ce contexte, une méthodologie permettant la formalisation et la caractérisation d'un modèle de fragilisation structurale est proposée. Ce modèle a pour objectif de simuler la rupture d'une plaque métallique perforée à un niveau macroscopique. La notion de fragilisation structurale est rappelée dans la première partie du mémoire. Engendrée par présence de perforations, celle-ci a une incidence directe sur la tenue mécanique des structures et elle est définie comme la distribution inhomogène des déformations le long du futur chemin de rupture. Le rapport de la déformation locale, observée le long de ce chemin, à une déformation de référence permet d'accéder à une "mesure" particulière de cette fragilisation. Sur la base d'observations expérimentales menées en quasi-statique sur des éprouvettes perforées ou non, le second chapitre tente de proposer un cadre théorique qui permet de mieux comprendre les fondements physiques de l'exercice de modélisation proposé. Le formalisme algébrique de Dvorak est ensuite mis en œuvre dans le troisième chapitre, pour poser les premiers jalons d'une méthode numérique multi-échelle de caractérisation du modèle de fragilisation structurale. Le développement de ce modèle, entrepris dans un premier temps dans le domaine élastique, a permis de démontrer la faisabilité d'une telle approche. Le développement de cette démarche en plasticité est ensuite tenté et discuté. Le quatrième chapitre cherche enfin à étudier l'influence de la dynamique sur le modèle de fragilisation structurale, via une étude expérimentale mettant en œuvre des matériaux sensibles ou non à la vitesse de déformation

Frequently hypercyclic operators.

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Invariant Gaussian measures for operators on Banach spaces and linear dynamics

International audienc

Modélisation multi-échelle d'un assemblage riveté aéronautique (vers un modèle de fragilisation structurale)

Dans le cadre de l'étude par éléments finis du crash des structures aéronautiques, la prédiction des modes de ruine engendrés au sein ou au voisinage des assemblages rivetés, telle la déchirure d'une tôle le long d'une ligne de rivets, s'avère, encore aujourd'hui, délicate. Dans ce contexte, une méthodologie permettant la formalisation et la caractérisation d'un modèle de fragilisation structurale est proposée. Ce modèle a pour objectif de simuler la rupture d'une plaque métallique perforée à un niveau macroscopique. La notion de fragilisation structurale est rappelée dans la première partie du mémoire. Engendrée par présence de perforations, celle-ci a une incidence directe sur la tenue mécanique des structures et elle est définie comme la distribution inhomogène des déformations le long du futur chemin de rupture. Le rapport de la déformation locale, observée le long de ce chemin, à une déformation de référence, permet d'accéder à une "mesure" particulière de cette fragilisation. Sur la base d'observations espérimentales menées en quasi-statique sur des éprouvettes perforées ou non, le second chapitre tente de proposer un cadre théorique qui permet de mieux comprendre les fondements physiques de l'exercice de modélisation proposé. Le formalisme algébrique de Dvorak est ensuite mis en oeuvre dans le troisième chapitre, pour poser les premiers jalons d'une méthode numérique multi-échelle de caractérisation du modèle de fragilisation structurale. Le développement de ce modèle, entrepris dans un premier temps dans le domaine élastique, a permis de démontrer la faisabilité d'une telle approche. Le développement de cette démarche en plasticité est ensuite tenté et discuté. Le quatrième chapitre cherche enfin à étudier l'influence de la dynamique sur le modèle de fragilisaton structurale, via une étude expérimentale mettant en oeuvre des matériaux sensibles ou non à la vitesse de déformationAs part of crash simulations, one difficulty concerns the representativeness of material and geometrical non-linear behaviours, especially in the jointed areas. For instance, the mechanical ruin of punched plates is not correctly predicted. In that sense, the aim of this work is to propose a methodology to formalize and characterize a structural embrittlement model, which will enable to model the structural weakening effects of holes in mettalic plates at a macroscopic level. The structural embrittlement concept is presented in the first part. Coming from the perforations, the structural embrittlement is defined as the inhomogeneous strain field along the future crack path. The local and nominal strain ratio observed along this crack path enables to measure the embrittlement phenomena. In the second part, the structural embrittlement mechanisms are analized from quasi-static experiments undertaken on punched and not punched samples. The embrittlement model is then formalized and a modelling task is carried out for a better understanding of physical basis of this model. The third part is devoted to the development of multiscale tool using a transformation field analysis approach in order to characterize the embrittlement model. The elastic developments have shown the feasibility of the method. The plastic behaviour is then implement in the multiscale model and discussed. Finally, the dependency of the structural model to strain rate is studied using dynamic experiments. Sensitive and insensitive materials are investigatedVALENCIENNES-BU Sciences Lettres (596062101) / SudocCACHAN-ENS (940162301) / SudocSudocFranceF

Common bounded universal functions for composition operators

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Bounded universal functions for sequences of holomorphic self-maps of the disk

International audienceWe give several characterizations of those sequences of holomorphic self-maps {phi(n)}(n >= 1) of the unit disk for which there exists a function F in the unit ball B={f is an element of H(infinity): parallel to f parallel to(infinity)= 1) admits a B-universal function if and only if phi is a parabolic or hyperbolic automorphism of D. We show that whenever there exists a B-universal function, then this function can be chosen to be a Blaschke product. Further, if there is a B-universal function, we show that there exist uniformly closed subspaces consisting entirely of universal functions