The Jacobian Conjecture: Some Steps towards Solution

Ludwik Drużkowski ()
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Ludwik Drużkowski: Jagiellonian University, Institute of Mathematics

A chapter in Automorphisms of Affine Spaces, 1995, pp 41-54 from Springer

Abstract: Abstract It is known that in the Generalized Jacobian Conjecture it is sufficient to consider only polynomial mappings of the form F = I − H, where H is a cubic homogeneous polynomial mapping. We present recent contributions to the problem, among others we show why the answer is positive for maps F = I − H, when H has only non-negative coefficients. We also point out the Global Stability Problem for polynomial transformations of ℝn, when n > 2 (note that for C 1 mappings the answer is positive if n = 2 and negative if n ≥ 4).

Keywords: Polynomial Mapping; Global Asymptotic Stability; Linear Differential Operator; Homogeneous Form; Newton Polygon (search for similar items in EconPapers)
Date: 1995
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-94-015-8555-2_2

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DOI: 10.1007/978-94-015-8555-2_2

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