The method of averaging for Poisson connections on foliations and its applications

IF 1 4区数学 Q3 MATHEMATICS, APPLIED

Journal of Geometric Mechanics Pub Date : 2020-01-01 DOI:10.3934/jgm.2020015

M. Avendaño-Camacho, Isaac Hasse-Armengol, E. Velasco-Barreras, Y. Vorobiev

引用次数: 1

Abstract

On a Poisson foliation equipped with a canonical and cotangential action of a compact Lie group, we describe the averaging method for Poisson connections. In this context, we generalize some previous results on Hannay-Berry connections for Hamiltonian and locally Hamiltonian actions on Poisson fiber bundles. Our main application of the averaging method for connections is the construction of invariant Dirac structures parametrized by the 2-cocycles of the de Rham-Casimir complex of the Poisson foliation.

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叶上泊松连接的平均方法及其应用

在具有紧李群的正则和共切作用的泊松叶上，我们描述了泊松连接的平均方法。在这种情况下，我们推广了前人关于汉纳-贝里连接对泊松纤维束的哈密顿作用和局部哈密顿作用的一些结果。我们对连接的平均方法的主要应用是构造由泊松叶理的de Rham-Casimir复形的2环参数化的不变Dirac结构。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Geometric Mechanics MATHEMATICS, APPLIED-PHYSICS, MATHEMATICAL

CiteScore

1.70

自引率

12.50%

发文量

审稿时长

>12 weeks

期刊介绍： The Journal of Geometric Mechanics (JGM) aims to publish research articles devoted to geometric methods (in a broad sense) in mechanics and control theory, and intends to facilitate interaction between theory and applications. Advances in the following topics are welcomed by the journal: 1. Lagrangian and Hamiltonian mechanics 2. Symplectic and Poisson geometry and their applications to mechanics 3. Geometric and optimal control theory 4. Geometric and variational integration 5. Geometry of stochastic systems 6. Geometric methods in dynamical systems 7. Continuum mechanics 8. Classical field theory 9. Fluid mechanics 10. Infinite-dimensional dynamical systems 11. Quantum mechanics and quantum information theory 12. Applications in physics, technology, engineering and the biological sciences.