Injective Polynomial Maps are Automorphisms

DOI10.2307/2974770zbMath0972.32015OpenAlexW4251424219WikidataQ114042680 ScholiaQ114042680MaRDI QIDQ4855783

Walter Rudin

Publication date: 21 November 2001

Published in: The American Mathematical Monthly (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2307/2974770

zbMATH Keywords

automorphismsJacobian conjectureinjective polynomial maps

Mathematics Subject Classification ID

Holomorphic mappings, (holomorphic) embeddings and related questions in several complex variables (32H02) Holomorphic maps on manifolds (58C10)

Related Items (21)

Remarks on the Jacobian conjecture ⋮ The first thirty years of Andersén-Lempert theory ⋮ On cubic-linear polynomial mappings ⋮ Keller Maps of Low Degree over Finite Fields ⋮ The Jacobian conjecture. II ⋮ Some reductions on Jacobian problem in two variables. ⋮ The inverse function theorem and the Jacobian conjecture for free analysis ⋮ Jet groups ⋮ Some remarks on the Jacobian conjecture and polynomial endomorphisms ⋮ Injectivity and almost global asymptotic stability of Hurwitz vector fields ⋮ Complex groups and root subgroup factorization ⋮ The divergence-free Jacobian conjecture in dimension two ⋮ Drużkowski matrix search and \(D\)-nilpotent automorphisms. ⋮ On quadratic Dehn functions. ⋮ Around Efimov's differential test for homeomorphism ⋮ Locally finite polynomial endomorphisms ⋮ Loops in SL(2, ℂ) and root subgroup factorization ⋮ Mathematical problems for the next century ⋮ Simple reasons why injective polynomial endomorphisms are automorphisms ⋮ Generalized Hénon maps: The cubic diffeomorphisms of the plane ⋮ Diffeomorphic real-analytic maps and the Jacobian conjecture.

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