STRUCTURE OF KELLER MAPPINGS, TWO-DIMENSIONAL CASE
A Keller map is a polynomial mapping ƒ : Rⁿ → Rⁿ (or Cⁿ → Cⁿ) with the Jacobian J_ƒ ≡ const ≠ 0. The Jacobian conjecture was first formulated by O. N. Keller in 1939. In the modern form it supposes injectivity of a Keller map. Earlier, in the case n = 2, the author gave a complete description of Kel...
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| Format: | Article |
| Language: | English |
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Petrozavodsk State University
2017-06-01
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| Series: | Проблемы анализа |
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| Online Access: | http://issuesofanalysis.petrsu.ru/article/genpdf.php?id=3870&lang=en |
| _version_ | 1823937822651842560 |
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| author | V. V. Starkov |
| author_facet | V. V. Starkov |
| author_sort | V. V. Starkov |
| collection | DOAJ |
| description | A Keller map is a polynomial mapping ƒ : Rⁿ → Rⁿ (or Cⁿ → Cⁿ) with the Jacobian J_ƒ ≡ const ≠ 0. The Jacobian conjecture was first formulated by O. N. Keller in 1939. In the modern form it supposes injectivity of a Keller map. Earlier, in the case n = 2, the author gave a complete description of Keller maps with deg ƒ ≤ 3. This paper is devoted to the description of Keller maps for which deg ƒ ≤ 4. Significant differences between these two cases are revealed, which, in particular, indicate the irregular structure of Keller maps even in the case of n = 2. |
| first_indexed | 2024-12-17T02:36:32Z |
| format | Article |
| id | doaj.art-ee4352bac5f54f9b9b8abebc750e9b34 |
| institution | Directory Open Access Journal |
| issn | 2306-3424 2306-3432 |
| language | English |
| last_indexed | 2024-12-17T02:36:32Z |
| publishDate | 2017-06-01 |
| publisher | Petrozavodsk State University |
| record_format | Article |
| series | Проблемы анализа |
| spelling | doaj.art-ee4352bac5f54f9b9b8abebc750e9b342022-12-21T22:06:50ZengPetrozavodsk State UniversityПроблемы анализа2306-34242306-34322017-06-016(24)110.15393/j3.art.2017.3870STRUCTURE OF KELLER MAPPINGS, TWO-DIMENSIONAL CASEV. V. Starkov0Petrozavodsk State UniversityA Keller map is a polynomial mapping ƒ : Rⁿ → Rⁿ (or Cⁿ → Cⁿ) with the Jacobian J_ƒ ≡ const ≠ 0. The Jacobian conjecture was first formulated by O. N. Keller in 1939. In the modern form it supposes injectivity of a Keller map. Earlier, in the case n = 2, the author gave a complete description of Keller maps with deg ƒ ≤ 3. This paper is devoted to the description of Keller maps for which deg ƒ ≤ 4. Significant differences between these two cases are revealed, which, in particular, indicate the irregular structure of Keller maps even in the case of n = 2.http://issuesofanalysis.petrsu.ru/article/genpdf.php?id=3870&lang=enJacobian conjectureKeller maps |
| spellingShingle | V. V. Starkov STRUCTURE OF KELLER MAPPINGS, TWO-DIMENSIONAL CASE Проблемы анализа Jacobian conjecture Keller maps |
| title | STRUCTURE OF KELLER MAPPINGS, TWO-DIMENSIONAL CASE |
| title_full | STRUCTURE OF KELLER MAPPINGS, TWO-DIMENSIONAL CASE |
| title_fullStr | STRUCTURE OF KELLER MAPPINGS, TWO-DIMENSIONAL CASE |
| title_full_unstemmed | STRUCTURE OF KELLER MAPPINGS, TWO-DIMENSIONAL CASE |
| title_short | STRUCTURE OF KELLER MAPPINGS, TWO-DIMENSIONAL CASE |
| title_sort | structure of keller mappings two dimensional case |
| topic | Jacobian conjecture Keller maps |
| url | http://issuesofanalysis.petrsu.ru/article/genpdf.php?id=3870&lang=en |
| work_keys_str_mv | AT vvstarkov structureofkellermappingstwodimensionalcase |