[Naissance de sous-variétés invariantes compactes attractives difféomorphes à des variétés moment-angle dans les familles génériques de dynamiques]
Toutes les intersections compactes de quadriques connues sous le nom de variétés moment-angle apparaissent comme attracteurs dans des bifurcations de Hopf généralisées.
All the compact intersections of quadrics known as moment-angle manifolds appear as attractors in generalized Hopf bifurcations.
Accepté le :
Publié le :
@article{CRMATH_2008__346_19-20_1099_0,
author = {Chaperon, Marc and L\'opez De Medrano, Santiago},
title = {Birth of attracting compact invariant submanifolds diffeomorphic to moment-angle manifolds in generic families of dynamics},
journal = {Comptes Rendus. Math\'ematique},
pages = {1099--1102},
publisher = {Elsevier},
volume = {346},
number = {19-20},
year = {2008},
doi = {10.1016/j.crma.2008.09.017},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2008.09.017/}
}
TY - JOUR AU - Chaperon, Marc AU - López De Medrano, Santiago TI - Birth of attracting compact invariant submanifolds diffeomorphic to moment-angle manifolds in generic families of dynamics JO - Comptes Rendus. Mathématique PY - 2008 SP - 1099 EP - 1102 VL - 346 IS - 19-20 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2008.09.017/ DO - 10.1016/j.crma.2008.09.017 LA - en ID - CRMATH_2008__346_19-20_1099_0 ER -
%0 Journal Article %A Chaperon, Marc %A López De Medrano, Santiago %T Birth of attracting compact invariant submanifolds diffeomorphic to moment-angle manifolds in generic families of dynamics %J Comptes Rendus. Mathématique %D 2008 %P 1099-1102 %V 346 %N 19-20 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2008.09.017/ %R 10.1016/j.crma.2008.09.017 %G en %F CRMATH_2008__346_19-20_1099_0
Chaperon, Marc; López De Medrano, Santiago. Birth of attracting compact invariant submanifolds diffeomorphic to moment-angle manifolds in generic families of dynamics. Comptes Rendus. Mathématique, Tome 346 (2008) no. 19-20, pp. 1099-1102. doi : 10.1016/j.crma.2008.09.017. http://www.numdam.org/articles/10.1016/j.crma.2008.09.017/
[1] Real quadrics in , complex manifolds and convex polytopes, Acta Math., Volume 197 (2006) no. 1, pp. 53-127
[2] Torus Actions and Their Applications in Topology and Combinatorics, University Lecture Series, vol. 24, Amer. Math. Soc., 2002
[3] Géométrie différentielle et singularités de systèmes dynamiques, Astérisque (1986), pp. 138-139
[4] -conjugacy of holomorphic flows near a singularity, Publ. Math. I.H.E.S., Volume 64 (1987), pp. 143-183
[5] Birth control in generalized Hopf bifurcations, C. R. Acad. Sci. Paris, Ser. I, Volume 345 (2007), pp. 453-458
[6] M. Chaperon, S. López de Medrano, Generalized Hopf bifurcations, in press
[7] More compact invariant manifolds appearing in the non-linear coupling of oscillators, C. R. Acad. Sci. Paris, Ser. I, Volume 342 (2006), pp. 301-305
[8] Convex polytopes, Coxeter orbifolds and torus actions, Duke Math. J., Volume 62 (1991) no. 2, pp. 417-451
[9] Persistence and smoothness of invariant manifolds for flows, Indiana Univ. Math. J., Volume 21 (1971), pp. 193-225
[10] Invariant Manifolds, Lecture Notes in Mathematics, vol. 583, Springer-Verlag, 1977
[11] The space of Siegel leaves of a holomorphic vector field, Dynamical Systems, Lecture Notes in Mathematics, vol. 1345, Springer-Verlag, 1988, pp. 233-245
[12] A new family of complex, compact, non-symplectic manifolds, Bol. Soc. Brasil. Mat., Volume 20 (1997), p. 2
[13] A new geometric construction of compact complex manifolds in any dimension, Math. Ann., Volume 317 (2000) no. 1, pp. 79-115
Cité par Sources :
