The index of singularities of vector fields and finite jets

Jaume Llibre; Radu Saghin

doi:10.1016/j.jde.2011.04.015

The index of singularities of vector fields and finite jets

Jaume Llibre, Radu Saghin

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

3 Scopus citations

Abstract

We describe when the index of a singularity of a smooth vector field is determined by a finite jet at the singularity. We also give some criteria to determine some terms from the formal series expansion of the vector field at the singularity which determine the index.

Original language	English
Pages (from-to)	2822-2832
Number of pages	11
Journal	Journal of Differential Equations
Volume	251
Issue number	10
DOIs	https://doi.org/10.1016/j.jde.2011.04.015
State	Published - 15 Nov 2011
Externally published	Yes

Keywords

Newton diagram
Topological index
Vector fields

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10.1016/j.jde.2011.04.015

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title = "The index of singularities of vector fields and finite jets",

abstract = "We describe when the index of a singularity of a smooth vector field is determined by a finite jet at the singularity. We also give some criteria to determine some terms from the formal series expansion of the vector field at the singularity which determine the index.",

keywords = "Newton diagram, Topological index, Vector fields",

author = "Jaume Llibre and Radu Saghin",

note = "Funding Information: The first author has been supported by the grants MCI/FEDER grant number MTM 2008-03437, CICYT grant number 2009-SGR410 and by ICREA Academia. The second author has been supported by Marie Curie IEF grant number 234559, and would like to thank CRM Barcelona for their hospitality.",

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doi = "10.1016/j.jde.2011.04.015",

language = "English",

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T1 - The index of singularities of vector fields and finite jets

AU - Llibre, Jaume

AU - Saghin, Radu

N1 - Funding Information: The first author has been supported by the grants MCI/FEDER grant number MTM 2008-03437, CICYT grant number 2009-SGR410 and by ICREA Academia. The second author has been supported by Marie Curie IEF grant number 234559, and would like to thank CRM Barcelona for their hospitality.

PY - 2011/11/15

Y1 - 2011/11/15

N2 - We describe when the index of a singularity of a smooth vector field is determined by a finite jet at the singularity. We also give some criteria to determine some terms from the formal series expansion of the vector field at the singularity which determine the index.

AB - We describe when the index of a singularity of a smooth vector field is determined by a finite jet at the singularity. We also give some criteria to determine some terms from the formal series expansion of the vector field at the singularity which determine the index.

KW - Newton diagram

KW - Topological index

KW - Vector fields

UR - http://www.scopus.com/inward/record.url?scp=80051953800&partnerID=8YFLogxK

U2 - 10.1016/j.jde.2011.04.015

DO - 10.1016/j.jde.2011.04.015

M3 - Article

AN - SCOPUS:80051953800

SN - 0022-0396

VL - 251

SP - 2822

EP - 2832

JO - Journal of Differential Equations

JF - Journal of Differential Equations

IS - 10

ER -

The index of singularities of vector fields and finite jets

Abstract

Keywords

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