Complete geometric invariant study of two classes of quadratic systems

Joan C. Artés; Jaume Llibre; Nicolae Vulpe

Complete geometric invariant study of two classes of quadratic systems

Joan C. Artés, Jaume Llibre, Nicolae Vulpe

Department of Mathematics

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

20 Citations (Scopus)

Abstract

In this article, using affine invariant conditions, we give a complete study for quadratic systems with center and for quadratic Hamiltonian systems. There are two improvements over the results in that studied centers up to GL-invariant, and over the results in that classified Hamiltonian quadratic systems without invariants. The geometrical affine invariant study presented here is a crucial step toward the goal of the invariant classification of all quadratic systems according to their singularities, finite and infinite. © 2012 Texas State University - San Marcos.

Original language	English
Pages (from-to)	1-35
Journal	Electronic Journal of Differential Equations
Volume	2012
Publication status	Published - 31 Jan 2012

Keywords

Quadratic vector fields
Type of singularity
Weak singularities

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title = "Complete geometric invariant study of two classes of quadratic systems",

abstract = "In this article, using affine invariant conditions, we give a complete study for quadratic systems with center and for quadratic Hamiltonian systems. There are two improvements over the results in that studied centers up to GL-invariant, and over the results in that classified Hamiltonian quadratic systems without invariants. The geometrical affine invariant study presented here is a crucial step toward the goal of the invariant classification of all quadratic systems according to their singularities, finite and infinite. {\textcopyright} 2012 Texas State University - San Marcos.",

keywords = "Quadratic vector fields, Type of singularity, Weak singularities",

author = "Art{\'e}s, {Joan C.} and Jaume Llibre and Nicolae Vulpe",

year = "2012",

month = jan,

day = "31",

language = "English",

volume = "2012",

pages = "1--35",

journal = "Electronic Journal of Differential Equations",

issn = "1072-6691",

publisher = "Texas State University - San Marcos",

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TY - JOUR

T1 - Complete geometric invariant study of two classes of quadratic systems

AU - Artés, Joan C.

AU - Llibre, Jaume

AU - Vulpe, Nicolae

PY - 2012/1/31

Y1 - 2012/1/31

N2 - In this article, using affine invariant conditions, we give a complete study for quadratic systems with center and for quadratic Hamiltonian systems. There are two improvements over the results in that studied centers up to GL-invariant, and over the results in that classified Hamiltonian quadratic systems without invariants. The geometrical affine invariant study presented here is a crucial step toward the goal of the invariant classification of all quadratic systems according to their singularities, finite and infinite. © 2012 Texas State University - San Marcos.

AB - In this article, using affine invariant conditions, we give a complete study for quadratic systems with center and for quadratic Hamiltonian systems. There are two improvements over the results in that studied centers up to GL-invariant, and over the results in that classified Hamiltonian quadratic systems without invariants. The geometrical affine invariant study presented here is a crucial step toward the goal of the invariant classification of all quadratic systems according to their singularities, finite and infinite. © 2012 Texas State University - San Marcos.

KW - Quadratic vector fields

KW - Type of singularity

KW - Weak singularities

M3 - Article

VL - 2012

SP - 1

EP - 35

JO - Electronic Journal of Differential Equations

JF - Electronic Journal of Differential Equations

SN - 1072-6691

ER -