An effective approach to Keller's Jacobian conjecture

DOI10.1007/BF01459126zbMath0504.13006OpenAlexW2046712067WikidataQ56481525 ScholiaQ56481525MaRDI QIDQ1835706

Ludwik M. Drużkowski

Publication date: 1983

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/163789

zbMATH Keywords

Jacobian conjecture

Mathematics Subject Classification ID

Jacobians, Prym varieties (14H40) Polynomials over commutative rings (13B25) Implicit function theorems; global Newton methods on manifolds (58C15)

Related Items (43)

On the Entrywise Powers of Matrices ⋮ Power linear Keller maps with ditto triangularizations ⋮ Irreducibility Properties of Keller Maps ⋮ Strong nilpotence holds in dimensions up to five only^∗ ⋮ Quantitative properties of the non-properness set of a polynomial map ⋮ On global diffeomorphisms of euclidian space ⋮ The jacobian conjecture: linear triangularizatlon for cubics in dimension three ⋮ Jacobian Conjecture and semi-algebraic maps ⋮ Foliations and global injectivity in \(\mathbb R^{n }\) ⋮ Some remarks on linear triangularizability ⋮ On cubic-linear polynomial mappings ⋮ A package of procedures and functions for construction and inversion of analytic mappings with unit Jacobian ⋮ On necessary and sufficient conditions for the real Jacobian conjecture ⋮ Bézoutians and injectivity of polynomial maps ⋮ A note on Jacobian problem over \(\mathbb{Z}\) ⋮ On the two-dimensional Jacobian conjecture: Magnus’ formula revisited, III ⋮ The linear triangularizability of some Keller maps ⋮ Polynomial maps with invertible sums of Jacobian matrices and directional derivatives ⋮ Some remarks on the Jacobian Conjecture and Drużkowski mappings ⋮ Unnamed Item ⋮ The Jacobian conjecture and injectivity conditions ⋮ Automorphisms of the k-algebra k[X1,…,Xm] ⋮ A note on the Jacobian conjecture ⋮ Quadratic linear Keller maps of nilpotency index three ⋮ Matrices with few nonzero principal minors ⋮ Eulerian operators and the Jacobian conjecture. III ⋮ Classification of Quadratic Homogeneous Automorphisms in Dimension Five ⋮ The Jacobian conjecture in case of rank or corank less than three ⋮ Drużkowski matrix search and \(D\)-nilpotent automorphisms. ⋮ Power linear Keller maps of rank two are linearly triangularizable ⋮ Cubic linear Keller maps ⋮ On the range of a Hadamard power of a positive semidefinite matrix ⋮ The linear dependence problem for power linear maps ⋮ Some Remarks on Polynomial Maps ⋮ Mappings with a composite part and with a constant Jacobian ⋮ Jacobian conjecture as a problem on integral points on affine curves ⋮ Faà di Bruno's formula and inversion of power series ⋮ A counterexample to Meisters' cubic-linear linearization conjecture ⋮ An ideal-theoretic approach to Keller maps ⋮ Quadratic linear Keller maps ⋮ Some co-tame automorphisms of affine spaces ⋮ Power linear Keller maps of dimension four ⋮ Algorithm for studying polynomial maps and reductions modulo prime number

Cites Work

• Unnamed Item
• A geometric approach to Keller's Jacobian conjecture
• Variazione continua ed omotopia in geometria algebrica
• Ein Satz über ganze Cremona-Transformationen der Ebene
• The Jacobian conjecture: Reduction of degree and formal expansion of the inverse
• Ganze Cremona-Transformationen

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