Quasi-homogeneous linearization of degenerate vector fields

被引：4

作者：

Algaba, A. ^{[1
]}

Garcia, C. ^{[1
]}

Reyes, M. ^{[1
]}

机构：

[1] Univ Huelva, Dept Integrated Sci, Ctr Adv Studies Phys Math & Computat, Huelva 21071, Spain

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2020年 / 483卷 / 02期

关键词：

Linearization of vector fields; Degenerate vector fields; Quadratic and cubic systems; INVERSE INTEGRATING FACTOR; INTEGRABILITY; EXISTENCE; SYSTEMS;

D O I：

10.1016/j.jmaa.2019.123635

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We characterize the analytic planar vector fields orbitally equivalent to its quasi-homogeneous leader term, by means the existence of a class of inverse integrating factors. Such a class of inverse integrating factors is determined by providing a normal form of two-dimensional scalar functions. This fact allows us to give some relevant criteria on t-linearization, analytical integrability and characterization of the centers for several families of planar vector fields. We study the systems whose leader term is quadratic or cubic and we analyze also a class of nilpotent systems. (C) 2019 Elsevier Inc. All rights reserved.

引用

页数：15

共 50 条

[21] Formal Normal Forms for the Perturbations of a Quasi-Homogeneous Hamiltonian Vector Field
E. Paul
[J]. Journal of Dynamical and Control Systems, 2004, 10 : 545 - 575
[22] Formal normal forms for the perturbations of a quasi-homogeneous Hamiltonian vector field
Paul, E
[J]. JOURNAL OF DYNAMICAL AND CONTROL SYSTEMS, 2004, 10 (04) : 545 - 575
[23] Spectral invariance in fields generated by quasi-homogeneous scaling law sources
Roychowdhury, H
Wolf, E
[J]. OPTICS COMMUNICATIONS, 2003, 215 (4-6) : 199 - 203
[24] Quasi-homogeneous Hilbert modules
Duan, Yongjiang
[J]. INTEGRAL EQUATIONS AND OPERATOR THEORY, 2007, 58 (03) : 301 - 314
[25] Asymptotically quasi-homogeneous distributions
Drozhzhinov, Yu. N.
Zavialov, B. I.
[J]. DOKLADY MATHEMATICS, 2008, 78 (01) : 503 - 507
[26] Asymptotically quasi-homogeneous distributions
Yu. N. Drozhzhinov
B. I. Zavialov
[J]. Doklady Mathematics, 2008, 78 : 503 - 507
[27] ON THE CLASSIFICATION OF QUASI-HOMOGENEOUS FUNCTIONS
KREUZER, M
SKARKE, H
[J]. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1992, 150 (01) : 137 - 147
[28] RADIOMETRY WITH QUASI-HOMOGENEOUS SOURCES
FOLEY, JT
WOLF, E
[J]. JOURNAL OF MODERN OPTICS, 1995, 42 (04) : 787 - 798
[29] Quasi-homogeneous normal forms
Algaba, A
Freire, E
Gamero, E
García, C
[J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2003, 150 (01) : 193 - 216
[30] QUASI-HOMOGENEOUS OVERLAP FUNCTIONS
Costa, L. M.
Bedregal, B. R. C.
[J]. DECISION MAKING AND SOFT COMPUTING, 2014, 9 : 294 - 299

← 1 2 3 4 5 →