自治哈密顿系统的对称性和守恒量综述

IF 1 4区数学 Q3 MATHEMATICS, APPLIED

Journal of Geometric Mechanics Pub Date : 2018-06-16 DOI:10.3934/JGM.2020009

N. Rom'an-Roy

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引用次数: 13

摘要

建立了自治哈密顿力学系统对称性的完整几何分类;解释如何在所有情况下获得它们相关的守恒量。特别地，我们首先回顾了关于哈密顿量和辛形式对称性的已知结果和性质，然后介绍和研究了一些新的非辛对称性及其守恒量。

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A summary on symmetries and conserved quantities of autonomous Hamiltonian systems

A complete geometric classification of symmetries of autonomous Hamiltonian mechanical systems is established; explaining how to obtain their associated conserved quantities in all cases. In particular, first we review well-known results and properties about the symmetries of the Hamiltonian and of the symplectic form and then some new kinds of non-symplectic symmetries and their conserved quantities are introduced and studied.

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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.