The asymptotic variety of a Pinchuk map as a polynomial curve

DOI10.1016/j.aml.2010.08.015zbMath1200.14112arXiv1001.3318OpenAlexW2007312566MaRDI QIDQ607149

L. Andrew Campbell

Publication date: 19 November 2010

Published in: Applied Mathematics Letters (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1001.3318

zbMATH Keywords

Jacobian conjectureasymptotic varietyreal polynomial map

Mathematics Subject Classification ID

Jacobian problem (14R15) Real algebraic sets (14P05)

Related Items (8)

A new qualitative proof of a result on the real jacobian conjecture ⋮ Pinchuk maps and function fields ⋮ Surjectivity of linear operators and semialgebraic global diffeomorphisms ⋮ Image of iterated polynomial maps of the real plane ⋮ Very degenerate polynomial submersions and counterexamples to the real Jacobian conjecture ⋮ A new class of non-injective polynomial local diffeomorphisms on the plane ⋮ On topological approaches to the Jacobian conjecture in ℂⁿ ⋮ A note on the Jacobian Conjecture

Cites Work

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• Jacobian pairs and Hamiltonian flows
• The geometry of the asymptotics of polynomial maps
• A counterexample to the strong real Jacobian conjecture
• Partial properness and real planar maps
• Polynomial automorphisms and the Jacobian conjecture
• Geometry of real polynomial mappings
• The variety of the asymptotic values of a real polynomial étale map
• Erratum to the Pinchuk map description in ``Partial properness and real planar maps
• Dedekind subrings of \(k[x_1,\dots,x_n\) are rings of polynomials]
• The set of points at which a polynomial map is not proper

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