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August 2009 A formula for the Łojasiewicz exponent at infinity in the real plane via real approximations
Ha Huy VUI, Nguyen Hong DUC
Hokkaido Math. J. 38(3): 417-425 (August 2009). DOI: 10.14492/hokmj/1258553971

Abstract

We compute the Łojasiewicz exponent of $f=(f_1,\ldots,f_n)\colon \Bbb R^2\to\Bbb R^n$ via the real approximation of Puiseux"s expansions at infinity of the curve $f_1\ldots f_n=0$. As a consequence we construct a collection of real meromorphic curves which provide a testing set for properness of $f$ as well as a condition, which is very easy to check, for a local diffeomorphism to be a global one.

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Ha Huy VUI. Nguyen Hong DUC. "A formula for the Łojasiewicz exponent at infinity in the real plane via real approximations." Hokkaido Math. J. 38 (3) 417 - 425, August 2009. https://doi.org/10.14492/hokmj/1258553971

Information

Published: August 2009
First available in Project Euclid: 18 November 2009

zbMATH: 1185.14057
MathSciNet: MR2548230
Digital Object Identifier: 10.14492/hokmj/1258553971

Subjects:
Primary: 14R25
Secondary: 14R25, 32A20, 32S05

Rights: Copyright © 2009 Hokkaido University, Department of Mathematics

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Vol.38 • No. 3 • August 2009
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