Hokkaido Mathematical Journal

A formula for the Łojasiewicz exponent at infinity in the real plane via real approximations

Ha Huy VUI and Nguyen Hong DUC

Full-text: Open access

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.

Article information

Source
Hokkaido Math. J., Volume 38, Number 3 (2009), 417-425.

Dates
First available in Project Euclid: 18 November 2009

Permanent link to this document
https://projecteuclid.org/euclid.hokmj/1258553971

Digital Object Identifier
doi:10.14492/hokmj/1258553971

Mathematical Reviews number (MathSciNet)
MR2548230

Zentralblatt MATH identifier
1185.14057

Subjects
Primary: 14R25: Affine fibrations [See also 14D06]
Secondary: 32A20: Meromorphic functions 32S05: Local singularities [See also 14J17] 14R25: Affine fibrations [See also 14D06]

Keywords
Łojasiewicz exponent at infinity Puiseux expansion at infinity Testing sets for properness of polynomial mappings

Citation

VUI, Ha Huy; DUC, Nguyen Hong. A formula for the Łojasiewicz exponent at infinity in the real plane via real approximations. Hokkaido Math. J. 38 (2009), no. 3, 417--425. doi:10.14492/hokmj/1258553971. https://projecteuclid.org/euclid.hokmj/1258553971


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