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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Polynomial-rational bijections of $ {\bf R}\sp n$


Authors: Krzysztof Kurdyka and Kamil Rusek
Journal: Proc. Amer. Math. Soc. 102 (1988), 804-808
MSC: Primary 14E05; Secondary 12D05, 14E07
MathSciNet review: 934846
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Abstract: It is shown in this note that every invertible polynomial transformation of $ {{\mathbf{R}}^n}$ of degree two has a rational inverse defined on the whole space $ {{\mathbf{R}}^n}$. The same is true for polynomial transformations of higher degrees, satisfying some differential condition which is a real analogue of Jagžev's condition considered in [3, 4, and 6].

The proofs of these statements are based on the Bialynicki-Birula and Rosenlicht surjectivity theorem [2] and on standard properties of complex dominant polynomial mappings.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1988-0934846-2
PII: S 0002-9939(1988)0934846-2
Article copyright: © Copyright 1988 American Mathematical Society