Abstract
Let F be a cubic homogeneous polynomial map from ℂn to ℂn with det JF = 1. Meisters conjectured that sF is linearizable for almost all s ∈ ℂ. We show that the conjecture is true if n ≤ 3 and false if n ≥ 4.
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References
E.-M.G.M. Hubbers, The Jacobian Conjecture: Cubic Homogeneous Maps in Dimension Four, Master’s thesis, University of Nijmegen, Toernooiveld, 6525 ED Nijmegen, The Netherlands, February 17 1994, directed by A.R.P. van den Essen.
G.H. Meisters, Dilated polyomorphisms conjugate to Dilations, Automorphisms of Affine Spaces (Curaçao) ( A.R.P. van den Essen, ed.), Caribbean Mathematics Foundation, Kluwer Academic Publishers, September 1994, Proceedings of the conference `Invertible Polynomial maps’.
D. Wright, The Jacobian Conjecture: linear triangularization for cubics in dimension three, Linear and Multilinear Algebra 34 (1993), 85–97.
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© 1995 Springer Science+Business Media Dordrecht
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van den Essen, A. (1995). A Counterexample to a Conjecture of Meisters. In: van den Essen, A. (eds) Automorphisms of Affine Spaces. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-8555-2_17
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DOI: https://doi.org/10.1007/978-94-015-8555-2_17
Publisher Name: Springer, Dordrecht
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