Endomorphisms of the plane sending linear coordinates to coordinates
Authors:
Charles ChingAn Cheng and Arno van den Essen
Journal:
Proc. Amer. Math. Soc. 128 (2000), 19111915
MSC (1991):
Primary 13B25, 13F20, 14E09, 16W20
Published electronically:
February 25, 2000
MathSciNet review:
1653437
Fulltext PDF Free Access
Abstract 
References 
Similar Articles 
Additional Information
Abstract: Let be a field of characteristic zero. We show that an endomorphism of which sends each linear coordinate to a coordinate is an automorphism of .
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 K. Adjamagbo and A. van den Essen, A resultant criterion and formula for the inversion of a polynomial map in two variables, J. of Pure and Applied Algebra 64 (1990), 16. MR 91g:14011
 [2]
 A. Choudary and A. Dimca, Complex Hypersurfaces diffeomorphic to affine spaces, preprint 1994. MR 95f:14084
 [3]
 A. van den Essen and V. Shpilrain, Some combinatorial questions about polynomial mappings, J. of Pure and Applied Algebra 119 (1997), 4752. MR 98g:13007
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 R. Feßler, A proof of the two dimensional MarkusYamabe stability conjecture, Annales Polonici Mathematici 62 (1995), 4575.
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 A. A. Glutsuk, The complete solution of the Jacobian problem for vector fields on the plane, Communications of the Moscow Mathematical Society, Russian Math. Surveys 49 (1994), 185186, Translated in Uspekhi Mat. Nauk, 3 (1994).
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 C. Gutierrez, A solution to the bidimensional global asymptotic stability conjecture, Ann. Inst. H. Poincaré Anal. Non Linéaire 12 (1995), 627671. MR 96k:34099b
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 J. H. McKay and S. S.S. Wang, An inversion formula for two polynomials in two variables, J. of Pure and Applied Algebra 40 (1986), 245257. MR 87j:12003
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 P. Rabier, On components of polynomial automorphisms in two variables, Comm. Algebra 24 (1996), 929937. MR 96m:14020
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Additional Information
Charles ChingAn Cheng
Affiliation:
Department of Mathematics, Oakland University, Rochester, Michigan 48309
Email:
cheng@oakland.edu
Arno van den Essen
Affiliation:
Department of Mathematics, University of Nijmegen, Nijmegen, The Netherlands
Email:
essen@sci.kun.nl
DOI:
http://dx.doi.org/10.1090/S0002993900052369
PII:
S 00029939(00)052369
Keywords:
Jacobian conjecture,
automorphism,
endomorphism,
derivation,
algebraically closed field,
coordinate
Received by editor(s):
December 12, 1997
Received by editor(s) in revised form:
September 1, 1998
Published electronically:
February 25, 2000
Communicated by:
Wolmer V. Vasconcelos
Article copyright:
© Copyright 2000
American Mathematical Society
