The index of singularities of vector fields and finite jets

被引：3

作者：

Llibre, Jaume ^{[2
]}

Saghin, Radu ^{[1
]}

机构：

[1] Ctr Recerca Matemat, Barcelona 08193, Catalunya, Spain

[2] Univ Autonoma Barcelona, Dept Matemat, E-08193 Barcelona, Catalunya, Spain

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2011年 / 251卷 / 10期

关键词：

Topological index; Vector fields; Newton diagram; STRUCTURAL STABILITY; NEWTON POLYHEDRA; CRITICAL-POINTS; INFINITY; PLANE;

D O I：

10.1016/j.jde.2011.04.015

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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. (C) 2011 Elsevier Inc. All rights reserved.

引用

页码：2822 / 2832

页数：11

共 50 条

[41] FINITELY DETERMINED SINGULARITIES OF FORMAL VECTOR-FIELDS
ICHIKAWA, F
INVENTIONES MATHEMATICAE, 1982, 66 (02) : 199 - 214
[42] Symmetric singularities of reversible vector fields in dimension three
Medrado, JCD
Teixeira, MA
PHYSICA D-NONLINEAR PHENOMENA, 1998, 112 (1-2) : 122 - 131
[43] On real center singularities of complex vector fields on surfaces
Leon, V.
Scardua, B.
DYNAMICAL SYSTEMS-AN INTERNATIONAL JOURNAL, 2024, 39 (02): : 231 - 242
[44] ABSOLUTELY ISOLATED SINGULARITIES OF HOLOMORPHIC VECTOR-FIELDS
CAMACHO, C
CANO, F
SAD, P
INVENTIONES MATHEMATICAE, 1989, 98 (02) : 351 - 369
[45] Higher order singularities in piecewise linear vector fields
Tricoche, X
Scheuermann, G
Hagen, H
MATHEMATICS OF SURFACES IX, 2000, : 99 - 113
[46] ORBITS OF FAMILIES OF VECTOR FIELDS AND INTEGRABILITY OF SYSTEMS WITH SINGULARITIES
SUSSMANN, HJ
BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 1973, 79 (01) : 197 - 199
[47] Desingularization of nilpotent singularities in families of planar vector fields
Panazzolo, D
MEMOIRS OF THE AMERICAN MATHEMATICAL SOCIETY, 2002, 158 (753) : v - +
[48] SYMMETRIES OF DEGENERATE CENTER SINGULARITIES OF PLANE VECTOR FIELDS
Maksymenko, S. I.
NONLINEAR OSCILLATIONS, 2009, 12 (04): : 522 - 542
[49] Causal conformal vector fields, and singularities of twistor spinors
Charles Frances
Annals of Global Analysis and Geometry, 2007, 32 : 277 - 295
[50] Solvability of planar complex vector fields with homogeneous singularities
Meziani, Abdelhamid
COMPLEX VARIABLES AND ELLIPTIC EQUATIONS, 2017, 62 (10) : 1447 - 1473

← 1 2 3 4 5 →