Algebraic and Computational Formulas for the Index of Real Analytic Vector Fields

作者：Castellanos Victor^*; Castorena Abel; Cruz Lopez Manuel

来源：Results in Mathematics, 2011, 59(1-2): 125-139.

DOI：10.1007/s00025-010-0066-9

• Real analytic vector fields
• complete intersection
• non algebraically isolated singularity
• Poincare-Hopf index

The signature formula of Eisenbud-Levine and Khimshiashvili for computing the Poincar,-Hopf index of a real analytic vector field at an algebraically isolated singularity is well known. We present in this paper an algebraic formula which allows to compute the index in the non-algebraically isolated case when the complex zeros associated to the complexified vector field have codimension one. We also analyse some instances in the codimension 2 case and describe a computer implementation that permits the calculation of the index in both the algebraically and non-algebraically isolated cases.

• 出版日期2011-2