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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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 |
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doaj-ee4352bac5f54f9b9b8abebc750e9b342021-07-02T09:33:30ZengPetrozavodsk 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 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
V. V. Starkov |
| spellingShingle |
V. V. Starkov STRUCTURE OF KELLER MAPPINGS, TWO-DIMENSIONAL CASE Проблемы анализа Jacobian conjecture Keller maps |
| author_facet |
V. V. Starkov |
| author_sort |
V. V. Starkov |
| title |
STRUCTURE OF KELLER MAPPINGS, TWO-DIMENSIONAL CASE |
| title_short |
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_sort |
structure of keller mappings, two-dimensional case |
| publisher |
Petrozavodsk State University |
| series |
Проблемы анализа |
| issn |
2306-3424 2306-3432 |
| publishDate |
2017-06-01 |
| 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. |
| topic |
Jacobian conjecture Keller maps |
| url |
http://issuesofanalysis.petrsu.ru/article/genpdf.php?id=3870&lang=en |
| work_keys_str_mv |
AT vvstarkov structureofkellermappingstwodimensionalcase |
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1721333035077468160 |