Poincaré renormalized forms
Gaeta, Giuseppe
Annales de l'I.H.P. Physique théorique, Tome 71 (1999), p. 461-514 / Harvested from Numdam
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Publié le : 1999-01-01
@article{AIHPA_1999__70_6_461_0,
     author = {Gaeta, Giuseppe},
     title = {Poincar\'e renormalized forms},
     journal = {Annales de l'I.H.P. Physique th\'eorique},
     volume = {71},
     year = {1999},
     pages = {461-514},
     mrnumber = {1693592},
     zbl = {0994.34024},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPA_1999__70_6_461_0}
}

Gaeta, Giuseppe. Poincaré renormalized forms. Annales de l'I.H.P. Physique théorique, Tome 71 (1999) pp. 461-514. http://gdmltest.u-ga.fr/item/AIHPA_1999__70_6_461_0/

[1] V.I. Arnold, Geometrical Methods in the Theory of Differential Equations, Springer, Berlin, 1988. | MR 947141

[2] V.I. Arnold and Yu.S. Il'Yashenko, Ordinary differential equations, in: D.V. Anosov and V.I. Arnold (Eds.), Encyclopaedia of Mathematical Sciences, Vol. I, Dynamical Systems I, Springer, Berlin, 1988, pp. 1-148. | MR 970794 | Zbl 0659.58012

[3] A.D. Bruno, Local Methods in Nonlinear Differential Equations, Springer, Berlin, 1989. | MR 993771 | Zbl 0674.34002

[4] M. Kummer, Nuovo Cimento B 1 (1971) 123. | MR 280107

[5] M. Kummer, Comm. Math. Phys. 48 (1976) 53. | MR 419948 | Zbl 0321.58017

[6] J.C. Van Der Meer, The Hamiltonian Hopf Bifurcation, Lecture Notes in Math., Vol. 1160, Springer, Berlin, 1985. | MR 815106 | Zbl 0585.58019

[7] H.W. Broer, Bifurcations of singularities in volume preserving vector fields, Ph.D. Thesis, Groningen, 1979; Formal normal form theorems for vector fields and some consequences for bifurcations in the volume preserving case, in: Lecture Notes Math., Vol. 898, Springer, Berlin, 1981. | MR 654883

[8] A. Baider and R.C. Churchill, Proc. Roy. Soc. Edinburgh A 108 (1988) 27. | Zbl 0671.58010

[9] A. Baider, J. Diff. Eqs. 78 (1989) 33. | MR 986152 | Zbl 0689.70005

[10] G. Gallavotti, Perturbation theory, mp-arc 93-318.

[11] G.B. Enettin, L. Galgani and A. Giorgilli, Nuovo Cimento B 79 (1984) 201.

[12] Yu.A. Mitropolsky and A.K. Lopatin, Nonlinear Mechanics, Groups and Symmetry, Kluwer, Dordrecht, 1995. | Zbl 0833.34002

[13] C. Elphick, E. Tirapegui, M.E. Brachet, P. Coullet and G. Iooss, Physica D 29 (1987) 95. | Zbl 0633.58020

[14] G. Iooss and M. Adelmeyer, Topics in Bifurcation Theory and Applications, World Scientific, Singapore, 1992. | MR 1177830 | Zbl 0833.34001

[15] V. Bargmann, Comm. Pure Appl. Math. 14 (1961) 187. | MR 157250 | Zbl 0107.09102

[16] G. Cicogna and G. Gaeta, J. Phys. A: Math. Gen. 27 (1994) 461; 27 (1994) 7115. | Zbl 0822.34037

[17] L.D. Landau and I.M. Lifshitz, Quantum Mechanics, Pergamon, London, 1959. | Zbl 0081.22207

[18] L.M. Markhashov, J. Appl. Math. Mech. 38 (1974) 788. | MR 377152 | Zbl 0359.34006

[19] A.D. Bruno and S. Walcher, J. Math. Anal. Appl. 183 (1994) 571; see also A.D. Bruno, Trans. Moscow Math. Soc. 25 (1971) 131; 26 (1971) 199. | MR 1274857 | Zbl 0804.34040

[20] G. Cicogna, J. Math. Anal. Appl. 199 (1996) 243; see also J. Phys. A: Math. Gen. 28 (1995) L179; 30 (1997) 6021; Nuovo Cim. B 113 (1998) 1425. | MR 1381390 | Zbl 0855.34042

[21] C.L. Siegel and J.K. Moser, Lectures on Celestial Mechanics, Springer, Berlin, 1955. (Reprinted in Classics in Mathematics, 1995.) | MR 1345153

[22] E. Forrest and D. Murray, Physica D 74 (1994) 181.

[23] G. Cicogna and G. Gaeta, Symmetry and perturbation theory for dynamical systems, Preprint IHES-P-97-12 (1997); revised and enlarged version to appear in Lect. Notes Phys., Springer. | MR 1892372

[24] G.R. Belitsky, Russ. Math. Surveys 33 (1978) 107; Funct. Anal. Appl. 20 (1986) 253.

[25] M. Golubitsky, D. Schaeffer and I. Stewart, Singularities and Groups in Bifurcation Theory, Vol. II, Springer, New York, 1988. | MR 950168 | Zbl 0691.58003