STRUCTURE OF KELLER MAPPINGS, TWO-DIMENSIONAL CASE
Journal Title: Проблемы анализа-Issues of Analysis - Year 2017, Vol 6, Issue 1
Abstract
A Keller map is a polynomial mapping ƒ : Rⁿ → Rⁿ (or Cⁿ → Cⁿ) with the Jacobian Jƒ ≡ 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.
Authors and Affiliations
V. V. Starkov
Keywords
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- EP ID EP225105
- DOI 10.15393/j3.art.2017.3870
- Views 107
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