Equivalence problem for compatible bi-Hamiltonian structures on three-dimensional orientable manifolds

被引：1

作者：

Bayrakdar, Tuna ^{[1
]}

Ergin, Abdullah Aziz ^{[1
]}

机构：

[1] Akdeniz Univ, Dept Math, Fac Sci, Antalya, Turkey

来源：

TURKISH JOURNAL OF MATHEMATICS | 2018年 / 42卷 / 05期

关键词：

Bi-Hamiltonian structure; Poisson structure; Cartan's method of equivalence; intransitive structure equations; Maurer-Cartan equations; ORDER LAGRANGIANS; INTEGRABILITY; SYSTEMS;

D O I：

10.3906/mat-1708-33

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We solve the equivalence problem for compatible bi-Hamiltonian structures on three-dimensional orientable manifolds via Cartan's method of equivalence. The problem separates into two branches on total space, one of which ends up with the intransitive involutive structure equations. For the transitive case, we obtain an {e}-structure on both total and base spaces.

引用

页码：2452 / 2465

页数：14

共 21 条

[1]

[Anonymous], CMS C P AM MATH SOC

[2]

[Anonymous], P 4 INT C DYN SYST D

[3]

[Anonymous], 2002, MATH SURVEYS MONOGRA

[4]

[Anonymous], 1989, CBMS NSF REGIONAL C

[5]

[Anonymous], 2006, THE J, DOI DOI 10.1007/S10958-006-0138-2

[6]

Cartan E., 1924, Bulletin de la Socit Mathmatique de France, V52, P205, DOI [10.24033/bsmf.1053, DOI 10.24033/BSMF.1053]

[7]

Cartan E., 1932, Annali di Matematica Pura ed Applicata, V11, P17, DOI [10.1007/BF02417822, DOI 10.1007/BF02417822]

[8] Equivalence problem and integrability of the Riccati equations [J].

Czyzycki, Tomasz ;

Hrivnak, Jiri .

NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS, 2010, 17 (03) :371-388

[9]

FELS ME, 1995, P LOND MATH SOC, V71, P221

[10] FEEDBACK EQUIVALENCE OF CONTROL-SYSTEMS [J].

GARDNER, RB ;

SHADWICK, WF .

SYSTEMS & CONTROL LETTERS, 1987, 8 (05) :463-465

← 1 2 3 →