About Formal Normal Form of the Semi-Hyperbolic Maps Germs on the Plane
There are consider the problem of constructing an analytical classification holomorphic resonance maps germs of Siegel-type in dimension 2. Namely, semi-hyperbolic maps of general form: such maps have one parabolic multiplier (equal to one), and the other hyperbolic (not equal in modulus to zero or...
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| Format: | Article |
| Language: | English |
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Irkutsk State University
2021-12-01
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| Series: | Известия Иркутского государственного университета: Серия "Математика" |
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| Online Access: | http://mathizv.isu.ru/en/article/file?id=1393 |
| _version_ | 1811190810220167168 |
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| author | P. A. Shaikhullina |
| author_facet | P. A. Shaikhullina |
| author_sort | P. A. Shaikhullina |
| collection | DOAJ |
| description | There are consider the problem of constructing an analytical classification holomorphic resonance maps germs of Siegel-type in dimension 2. Namely, semi-hyperbolic maps of general form: such maps have one parabolic multiplier (equal to one), and the other hyperbolic (not equal in modulus to zero or one). In this paper, the first stage of constructing an analytical classification by the method of functional invariants is carried out: a theorem on the reducibility of a germ to its formal normal form by "semiformal" changes of coordinates is proved. The one-time shift along the saddle node vector field (the formal normal form in the problem of the analytical classification of saddle-node vector fields on a plane) is chosen as the formal normal form. |
| first_indexed | 2024-04-11T14:55:20Z |
| format | Article |
| id | doaj.art-d1e46c1abe2c41629fe5078d9b6fddca |
| institution | Directory Open Access Journal |
| issn | 1997-7670 2541-8785 |
| language | English |
| last_indexed | 2024-04-11T14:55:20Z |
| publishDate | 2021-12-01 |
| publisher | Irkutsk State University |
| record_format | Article |
| series | Известия Иркутского государственного университета: Серия "Математика" |
| spelling | doaj.art-d1e46c1abe2c41629fe5078d9b6fddca2022-12-22T04:17:16ZengIrkutsk State UniversityИзвестия Иркутского государственного университета: Серия "Математика"1997-76702541-87852021-12-013815464https://doi.org/10.26516/1997-7670.2021.38.54About Formal Normal Form of the Semi-Hyperbolic Maps Germs on the PlaneP. A. ShaikhullinaThere are consider the problem of constructing an analytical classification holomorphic resonance maps germs of Siegel-type in dimension 2. Namely, semi-hyperbolic maps of general form: such maps have one parabolic multiplier (equal to one), and the other hyperbolic (not equal in modulus to zero or one). In this paper, the first stage of constructing an analytical classification by the method of functional invariants is carried out: a theorem on the reducibility of a germ to its formal normal form by "semiformal" changes of coordinates is proved. The one-time shift along the saddle node vector field (the formal normal form in the problem of the analytical classification of saddle-node vector fields on a plane) is chosen as the formal normal form.http://mathizv.isu.ru/en/article/file?id=1393semi-hyperbolic mapsformal classificationanalytical classification |
| spellingShingle | P. A. Shaikhullina About Formal Normal Form of the Semi-Hyperbolic Maps Germs on the Plane Известия Иркутского государственного университета: Серия "Математика" semi-hyperbolic maps formal classification analytical classification |
| title | About Formal Normal Form of the Semi-Hyperbolic Maps Germs on the Plane |
| title_full | About Formal Normal Form of the Semi-Hyperbolic Maps Germs on the Plane |
| title_fullStr | About Formal Normal Form of the Semi-Hyperbolic Maps Germs on the Plane |
| title_full_unstemmed | About Formal Normal Form of the Semi-Hyperbolic Maps Germs on the Plane |
| title_short | About Formal Normal Form of the Semi-Hyperbolic Maps Germs on the Plane |
| title_sort | about formal normal form of the semi hyperbolic maps germs on the plane |
| topic | semi-hyperbolic maps formal classification analytical classification |
| url | http://mathizv.isu.ru/en/article/file?id=1393 |
| work_keys_str_mv | AT pashaikhullina aboutformalnormalformofthesemihyperbolicmapsgermsontheplane |