Geodesic
Normal forms of multidimesional parabolic mappings
Vestnik Chelyabinskogo Gosudarstvennogo Universiteta. Matematika, Mekhanika, Informatika, no. 15 (2012), pp. 71-79 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

In the paper there is considered formal classification of germs of analytic mappings in the plane with identity linear part. It is shown that under some generality restrictions on its 2-jet, the germ is strictly formally equivalent to a quasipolynomial normal form of a special type. The uniqueness of such normal forms is established.
Keywords: normal forms, parabolic maps
Mots-clés : formal classification. 
@article{VCHGU_2012_15_a4,
     author = {I. V. Korovina},
     title = {Normal forms of multidimesional parabolic mappings},
     journal = {Vestnik Chelyabinskogo Gosudarstvennogo Universiteta. Matematika, Mekhanika, Informatika},
     pages = {71--79},
     year = {2012},
     number = {15},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VCHGU_2012_15_a4/}
}
TY  - JOUR
AU  - I. V. Korovina
TI  - Normal forms of multidimesional parabolic mappings
JO  - Vestnik Chelyabinskogo Gosudarstvennogo Universiteta. Matematika, Mekhanika, Informatika
PY  - 2012
SP  - 71
EP  - 79
IS  - 15
UR  - http://geodesic.mathdoc.fr/item/VCHGU_2012_15_a4/
LA  - ru
ID  - VCHGU_2012_15_a4
ER  - 
%0 Journal Article
%A I. V. Korovina
%T Normal forms of multidimesional parabolic mappings
%J Vestnik Chelyabinskogo Gosudarstvennogo Universiteta. Matematika, Mekhanika, Informatika
%D 2012
%P 71-79
%N 15
%U http://geodesic.mathdoc.fr/item/VCHGU_2012_15_a4/
%G ru
%F VCHGU_2012_15_a4
I. V. Korovina. Normal forms of multidimesional parabolic mappings. Vestnik Chelyabinskogo Gosudarstvennogo Universiteta. Matematika, Mekhanika, Informatika, no. 15 (2012), pp. 71-79. http://geodesic.mathdoc.fr/item/VCHGU_2012_15_a4/

[1] V. I. Arnold, Dopolnitelnye glavy teorii obyknovennykh differentsialnykh uravnenii, Nauka, M., 1978 | MR

[2] S. M. Voronin, “Analiticheskaya klassifikatsiya rostkov konformnykh otobrazhenii $(\mathbb{C},0)\rightarrow (\mathbb{C},0)$ s tozhdestvennoi lineinoi chastyu”, Funktsion. analiz, 15:1 (1981), 1–17 | Zbl

[3] L. Ortiz-Bobadilla, E. Rosales-Gonzales, S. M. Voronin, “Rigidity theorem for degenerated singular points of germs of holomorphic vector fields in the complex plane”, J. Dynam. Control Systems, 7:4 (2001), 553–599 | DOI | MR | Zbl

[4] L. Ortiz-Bobadilla, E. Rosales-Gonzales, S. M. Voronin, “Rigidity theorem for degenerated singular points of germs of dicritic holomorphic vector fields in the complex plane”, Moscow Math. J., 5:1 (2005), 171–206 | MR | Zbl

[5] L. Ortiz-Bobadilla, E. Rosales-Gonzales, S. M. Voronin, “Analytic normal forms of germs of holomorphic dicritic foliations”, Moscow Math. J., 8:3 (2008), 521–545 | MR | Zbl

[6] S.M. Voronin, L. Ortis-Bobadilla, E. Rosales-Gonsales, “Problema Toma v zadache ob orbitalnoi analiticheskoi klassifikatsii vyrozhdennykh osobykh tochek golomorfnykh vektornykh polei na ploskosti”, Dokl. Akad. nauk, 434:4 (2010), 443–446 | Zbl

[7] L. Ortiz-Bobadilla, E. Rosales-Gonzales, S. M. Voronin, Thom's problem for generic degenerated singular points of holomorphic foliations in the plane, Preliminares del Instituto de Matematicas, UNAM, No 867, 2010 | MR