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ON THE RELATION BETWEEN INDEX AND MULTIPLICITY

Published online by Cambridge University Press:  01 June 1998

ANNA CIMA ,
ARMENGOL GASULL  and
JOAN TORREGROSA
ANNA CIMA
Affiliation:
Departament de Matemàtiques, Edifici C, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona, Spain
ARMENGOL GASULL
Affiliation:
Departament de Matemàtiques, Edifici C, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona, Spain
JOAN TORREGROSA
Affiliation:
Departament de Matemàtiques, Edifici C, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona, Spain
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Abstract

This paper is mainly devoted to the study of the index of a map at a zero, and the index of a polynomial map over ℝn. For semi-quasi-homogeneous maps we prove that the index at a zero coincides with the index at this zero of its quasi-homogeneous part. For a class of polynomial maps with finite zero set we provide a method which makes easier the computation of its index over ℝn. Finally we relate the index and the multiplicity.

Type
Notes and Papers
Information
Journal of the London Mathematical Society , Volume 57 , Issue 3 , June 1998 , pp. 757 - 768
Copyright
The London Mathematical Society 1998

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