Growth at infinity and index of polynomial maps

Carles Bivià-Ausina; Jorge A.C. Huarcaya

doi:10.1016/j.jmaa.2014.09.062

Growth at infinity and index of polynomial maps

Carles Bivià-Ausina, Jorge A.C. Huarcaya

Dynamical systems, differential equations and their applications

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

Let F : Kⁿ → Kⁿ be a polynomial map such that F^-1(0) is compact, where K = R or C. Then we give a condition implying that there is a uniform bound for the Łojasiewicz exponent at infinity in certain deformations of F. This fact gives a result about the invariance of the global index of F.

Original language	English
Pages (from-to)	1414-1433
Number of pages	20
Journal	Journal of Mathematical Analysis and Applications
Volume	422
Issue number	2
DOIs	https://doi.org/10.1016/j.jmaa.2014.09.062
State	Published - 15 Feb 2015

Bibliographical note

Publisher Copyright:
© 2014 Elsevier Inc.

Keywords

Newton polyhedron
Polynomial vector fields
Topological index
Łojasiewicz exponent at infinity

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10.1016/j.jmaa.2014.09.062

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title = "Growth at infinity and index of polynomial maps",

abstract = "Let F : Kn → Kn be a polynomial map such that F-1(0) is compact, where K = R or C. Then we give a condition implying that there is a uniform bound for the {\L}ojasiewicz exponent at infinity in certain deformations of F. This fact gives a result about the invariance of the global index of F.",

keywords = "Newton polyhedron, Polynomial vector fields, Topological index, {\L}ojasiewicz exponent at infinity",

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AU - Bivià-Ausina, Carles

AU - Huarcaya, Jorge A.C.

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N2 - Let F : Kn → Kn be a polynomial map such that F-1(0) is compact, where K = R or C. Then we give a condition implying that there is a uniform bound for the Łojasiewicz exponent at infinity in certain deformations of F. This fact gives a result about the invariance of the global index of F.

AB - Let F : Kn → Kn be a polynomial map such that F-1(0) is compact, where K = R or C. Then we give a condition implying that there is a uniform bound for the Łojasiewicz exponent at infinity in certain deformations of F. This fact gives a result about the invariance of the global index of F.

KW - Newton polyhedron

KW - Polynomial vector fields

KW - Topological index

KW - Łojasiewicz exponent at infinity

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DO - 10.1016/j.jmaa.2014.09.062

M3 - Artículo

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VL - 422

SP - 1414

EP - 1433

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 2

ER -

Growth at infinity and index of polynomial maps

Abstract

Bibliographical note

Keywords

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