ON BI-INTEGRABLE NATURAL HAMILTONIAN SYSTEMS ON RIEMANNIAN MANIFOLDS

被引：20

作者：

Tsiganov, A. V. ^{[1
]}

机构：

[1] St Petersburg State Univ, Dept Computat Phys, St Petersburg 198504, Russia

来源：

JOURNAL OF NONLINEAR MATHEMATICAL PHYSICS | 2011年 / 18卷 / 02期

关键词：

Integrable system; Riemannian manifold; bi-hamiltonian geometry; VARIABLE SEPARATION; KILLING TENSORS; BIHAMILTONIAN STRUCTURES; POISSON BRACKETS; ORDER INTEGRALS; JACOBI EQUATION; TODA; SEPARABILITY;

D O I：

10.1142/S1402925111001507

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We introduce the concept of natural Poisson bivectors, which generalizes the Benenti approach to construction of natural integrable systems on Riemannian manifolds and allows us to consider almost the whole known zoo of integrable systems in framework of bi-hamiltonian geometry.

引用

页码：245 / 268

页数：24

共 50 条

[21] Stochastic dynamical systems developed on Riemannian manifolds
Mamajiwala, Mariya
Roy, Debasish
PROBABILISTIC ENGINEERING MECHANICS, 2022, 67
[22] Eigenvalues of the bi-Xin-Laplacian on complete Riemannian manifolds
Hao, Xiaotian
Zeng, Lingzhong
COMMUNICATIONS IN ANALYSIS AND MECHANICS, 2023, 15 (02): : 162 - 176
[23] A NATURAL CONNECTION ON A BASIC CLASS OF RIEMANNIAN PRODUCT MANIFOLDS
Gribacheva, Dobrinka
INTERNATIONAL JOURNAL OF GEOMETRIC METHODS IN MODERN PHYSICS, 2012, 9 (07)
[24] Coulomb Systems on Riemannian Manifolds and Stability of Matter
Alberto Enciso
Annales Henri Poincaré, 2011, 12 : 723 - 741
[25] Commutative partially integrable systems on Poisson manifolds
Kurov, A. V.
MOSCOW UNIVERSITY PHYSICS BULLETIN, 2016, 71 (04) : 375 - 380
[26] Commutative partially integrable systems on Poisson manifolds
A. V. Kurov
Moscow University Physics Bulletin, 2016, 71 : 375 - 380
[27] Separation of variables for integrable systems on Poisson manifolds
A. V. Tsiganov
Physics of Atomic Nuclei, 2002, 65 : 1128 - 1134
[28] An integrable extension of TD hierarchy and generalized bi-Hamiltonian structures
Liu, Huan
Geng, Xianguo
MODERN PHYSICS LETTERS B, 2015, 29 (21):
[29] A NEW HIERARCHY OF INTEGRABLE SYSTEMS AND ITS HAMILTONIAN STRUCTURE
屠规彰
Science China Mathematics, 1989, (02) : 142 - 153
[30] On the governing equations of motion of nonholonomic systems on Riemannian manifolds
Liu X.
Journal of Mathematical Sciences, 2011, 177 (3) : 411 - 418

← 1 2 3 4 5 →