[Réduction simultanée aux formes normales de champs de vecteurs singuliers commutatifs avec des parties linéaires ayant des blocs de Jordan]
Nous étudions la linéarisation simultanée de
We study the simultaneous linearizability of
Keywords: singular vector field, linearization, Jordan block, homological equation, Diophantine conditions, Gevrey spaces, decomposition
Mots-clés : champ de vecteurs singulier, linéarisation, bloc de Jordan, équations omologiques, conditions diophantiennes, espaces de Gevrey, décomposition
Yoshino, Masafumi 1 ; Gramchev, Todor 2
@article{AIF_2008__58_1_263_0, author = {Yoshino, Masafumi and Gramchev, Todor}, title = {Simultaneous reduction to normal forms of commuting singular vector fields with linear parts having {Jordan} blocks}, journal = {Annales de l'Institut Fourier}, pages = {263--297}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {58}, number = {1}, year = {2008}, doi = {10.5802/aif.2350}, mrnumber = {2401222}, zbl = {1137.37025}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.2350/} }
TY - JOUR AU - Yoshino, Masafumi AU - Gramchev, Todor TI - Simultaneous reduction to normal forms of commuting singular vector fields with linear parts having Jordan blocks JO - Annales de l'Institut Fourier PY - 2008 SP - 263 EP - 297 VL - 58 IS - 1 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.2350/ DO - 10.5802/aif.2350 LA - en ID - AIF_2008__58_1_263_0 ER -
%0 Journal Article %A Yoshino, Masafumi %A Gramchev, Todor %T Simultaneous reduction to normal forms of commuting singular vector fields with linear parts having Jordan blocks %J Annales de l'Institut Fourier %D 2008 %P 263-297 %V 58 %N 1 %I Association des Annales de l’institut Fourier %U https://aif.centre-mersenne.org/articles/10.5802/aif.2350/ %R 10.5802/aif.2350 %G en %F AIF_2008__58_1_263_0
Yoshino, Masafumi; Gramchev, Todor. Simultaneous reduction to normal forms of commuting singular vector fields with linear parts having Jordan blocks. Annales de l'Institut Fourier, Tome 58 (2008) no. 1, pp. 263-297. doi : 10.5802/aif.2350. https://aif.centre-mersenne.org/articles/10.5802/aif.2350/
[1] Diagonalization of nondiagonalizable discrete holomorphic dynamical systems, Amer. J. Math., Volume 122 (2000), pp. 757-781 | DOI | MR | Zbl
[2] Geometrical Methods in the Theory of Ordinary Differential Equations, Springer, 1983 | MR | Zbl
[3] The analytic form of differential equations, Tr. Mosk. Mat. O-va (1971) no. 25, pp. 119-262 and 26, 199–239 (1972) (in Russian); see also Trans. Mosc. Math. Soc. 25, 131-288 (1971) and 26, 199-239 (1972) | Zbl
[4] Symmetries and convergence of normalizing transformations, J. Math. Anal. Appl., Volume 183 (1994), pp. 571-576 | DOI | MR | Zbl
[5] Exponentially long time stability for non-linearizable analytic germs of
[6] Linearization of analytic and non-analytic germs of diffeomorphisms of
[7] Diffeomorphisms:
[8] Symmetry and perturbation theory in nonlinear dynamics, New Series m: Monographs, 57, Springer–Verlag, 1999 | MR | Zbl
[9] Convergence of normal form transformations: the role of symmetries. Symmetry and perturbation theory, Acta Math. Appl., Volume 70 (2002), pp. 95-111 | DOI | MR | Zbl
[10] A tutorial on KAM theory. (1999) | Zbl
[11] Biholomorphic maps with linear parts having Jordan blocks: Linearization and resonance type phenomena, Math. Physics Electronic Journal, Volume 8 (2002) no. paper n. 2, pp. 1-27 | MR | Zbl
[12] Perturbations of vector fields on tori: resonant normal forms and Diophantine phenomena, Proc. Edinb. Math. Soc. (2), Volume 45 (2002) no. 3, p. 731-159 | DOI | MR | Zbl
[13] Smooth linearization of germs of
[14] The theory of matrices, 1-2, Chelsea Publishing Co., New York, 1959 | MR | Zbl
[15] On the linearization of holomorphic vector fields in the Siegel Domain with linear parts having nontrivial Jordan blocks, World Scientific (2003), pp. 106-115 (S. Abenda, G. Gaeta and S. Walcher eds, Symmetry and perturbation theory, Cala Gonone, 16–22 May 2002) | MR
[16] Sur la conjugaison différentiable des difféomorphismes du cercle à des rotations, Publ. Math. I.H.É.S., Volume 49 (1979), pp. 5-233 | Numdam | MR | Zbl
[17] Higher cohomology for Abelian groups of toral automorphisms, Ergodic Theory Dyn. Syst., Volume 15 (1995) no. 3, pp. 569-592 | DOI | MR | Zbl
[18] Non linearizable holomorphic dynamics having an uncountable number of symmetries, Inv. Math., Volume 119 (1995), pp. 67-127 | DOI | MR | Zbl
[19] Total convergence or small divergence in small divisors, Commun. Math. Phys., Volume 223 (2001) no. 3, pp. 451-464 | DOI | MR | Zbl
[20] On commuting circle mappings and simultaneous Diophantine approximations, Mathematische Zeitschrift, Volume 205 (1990), pp. 105-121 | DOI | MR | Zbl
[21] Modèles locaux de champs et de formes, 30, Astérisque, 1975 | Zbl
[22] Modèles locaux de champs et de formes, Lect. Notes in Mathematics, 785, Springer Verlag, 1980
[23] The structure of local homeomorphisms II, III, Amer. J. Math. (1958), pp. 623-632 (80, 623-632 and 81, 578–604) | DOI | MR | Zbl
[24] Singular complete integrability, Publ. Math. I.H.E.S., Volume 91 (2000), pp. 134-210 | Numdam | MR | Zbl
[25] Normalisation holomorphe d’algèbres de type Cartan de champs de vecteurs holomorphes singuliers, Ann. Math., Volume 161 (2005), pp. 589-612 | DOI | Zbl
[26] On convergent normal form transformations in presence of symmetries, J. Math. Anal. Appl., Volume 244 (2000), pp. 17-26 | DOI | MR | Zbl
[27] A remark on Siegel’s theorem for nondiagonalizable linear part, Astérisque, Volume 231 (1995), pp. 3-88 (manuscript, 1978, see also Théorème de Siegel, nombres de Bruno et polynômes quadratiques)
[28] Simultaneous normal forms of commuting maps and vector fields, World Scientific, Singapore (1999), pp. 287-294 (A. Degasperis, G. Gaeta eds., Symmetry and perturbation theory SPT 98, Rome 16–22 December 1998) | MR | Zbl
[29] Convergence versus integrability in Poincaré-Dulac normal form., Math. Res. Lett., Volume 9 (2002) no. 2-3, pp. 217-228 | MR | Zbl
- Perturbation of Systems with Nilpotent Real Part, Encyclopedia of Complexity and Systems Science (2013), p. 1 | DOI:10.1007/978-3-642-27737-5_395-4
- Perturbation of Systems with Nilpotent Real Part, Mathematics of Complexity and Dynamical Systems (2012), p. 1276 | DOI:10.1007/978-1-4614-1806-1_78
- Perturbation of Systems with Nilpotent Real Part, Encyclopedia of Complexity and Systems Science (2009), p. 6649 | DOI:10.1007/978-0-387-30440-3_395
- Progress in normal form theory, Nonlinearity, Volume 22 (2009) no. 7, p. R77 | DOI:10.1088/0951-7715/22/7/r01
- Perturbation of Systems with Nilpotent Real Part, Perturbation Theory (2009), p. 211 | DOI:10.1007/978-1-0716-2621-4_395
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