Center configurations of Hamiltonian cubic systems

Research output: Contribution to journalArticle

Abstract

Second order eyes of Hamiltonian cubic systems are classified into seven classes based on the orientation of the cycles within these eyes. They are further categorized into nine Conti classes based on the structure of the separatrix cycles that bound them. Examples of systems of each type are presented, and examples of third and fourth order eyes are also given. The classification is connected to part of Hilbert's sixteenth problem which asks for the possible relative positions of cycles in an autonomous polynomial system in the plane.

Original languageEnglish (US)
Pages (from-to)1111-1122
Number of pages12
JournalRocky Mountain Journal of Mathematics
Volume40
Issue number4
DOIs
StatePublished - 2010

Fingerprint

Cycle
Configuration
Separatrix
Polynomial Systems
Autonomous Systems
Hilbert
Fourth Order
Class

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Center configurations of Hamiltonian cubic systems. / Blows, Terence R.

In: Rocky Mountain Journal of Mathematics, Vol. 40, No. 4, 2010, p. 1111-1122.

Research output: Contribution to journalArticle

@article{cb7f11ec3b534ade9fba5471a7f8a1ae,
title = "Center configurations of Hamiltonian cubic systems",
abstract = "Second order eyes of Hamiltonian cubic systems are classified into seven classes based on the orientation of the cycles within these eyes. They are further categorized into nine Conti classes based on the structure of the separatrix cycles that bound them. Examples of systems of each type are presented, and examples of third and fourth order eyes are also given. The classification is connected to part of Hilbert's sixteenth problem which asks for the possible relative positions of cycles in an autonomous polynomial system in the plane.",
author = "Blows, {Terence R}",
year = "2010",
doi = "10.1216/RMJ-2010-40-4-1111",
language = "English (US)",
volume = "40",
pages = "1111--1122",
journal = "Rocky Mountain Journal of Mathematics",
issn = "0035-7596",
publisher = "Rocky Mountain Mathematics Consortium",
number = "4",

}

TY - JOUR

T1 - Center configurations of Hamiltonian cubic systems

AU - Blows, Terence R

PY - 2010

Y1 - 2010

N2 - Second order eyes of Hamiltonian cubic systems are classified into seven classes based on the orientation of the cycles within these eyes. They are further categorized into nine Conti classes based on the structure of the separatrix cycles that bound them. Examples of systems of each type are presented, and examples of third and fourth order eyes are also given. The classification is connected to part of Hilbert's sixteenth problem which asks for the possible relative positions of cycles in an autonomous polynomial system in the plane.

AB - Second order eyes of Hamiltonian cubic systems are classified into seven classes based on the orientation of the cycles within these eyes. They are further categorized into nine Conti classes based on the structure of the separatrix cycles that bound them. Examples of systems of each type are presented, and examples of third and fourth order eyes are also given. The classification is connected to part of Hilbert's sixteenth problem which asks for the possible relative positions of cycles in an autonomous polynomial system in the plane.

UR - http://www.scopus.com/inward/record.url?scp=77958472664&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77958472664&partnerID=8YFLogxK

U2 - 10.1216/RMJ-2010-40-4-1111

DO - 10.1216/RMJ-2010-40-4-1111

M3 - Article

AN - SCOPUS:77958472664

VL - 40

SP - 1111

EP - 1122

JO - Rocky Mountain Journal of Mathematics

JF - Rocky Mountain Journal of Mathematics

SN - 0035-7596

IS - 4

ER -