交折射、余折射、接触和共接触哈密顿系统的四元数的列积分性

IF 1 4区物理与天体物理 Q3 PHYSICS, MATHEMATICAL

Reports on Mathematical Physics Pub Date : 2024-02-01 DOI:10.1016/S0034-4877(24)00009-0

R. Azuaje

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引用次数: 0

摘要

在本文中，我们提出了交错流形和接触流形上与时间无关的哈密顿系统，以及共交错流形和共接触流形上与时间有关的哈密顿系统的Lie积分性定理。我们证明，哈密顿系统运动常数的可解李代数等同于定义系统动力学的矢量场对称性的可解李代数，这使我们能够通过正交找到运动方程的解。

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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Lie integrability by quadratures for symplectic, cosymplectic, contact and cocontact Hamiltonian systems

In this paper we present the theorem on Lie integrability by quadratures for time-independent Hamiltonian systems on symplectic and contact manifolds, and for time-dependent Hamiltonian systems on cosymplectic and cocontact manifolds. We show that having a solvable Lie algebra of constants of motion for a Hamiltonian system is equivalent to having a solvable Lie algebra of symmetries of the vector field defining the dynamics of the system, which allows us to find solutions of the equations of motion by quadratures.

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来源期刊

Reports on Mathematical Physics 物理-物理：数学物理

CiteScore

1.80

自引率

0.00%

发文量

审稿时长

6 months

期刊介绍： Reports on Mathematical Physics publish papers in theoretical physics which present a rigorous mathematical approach to problems of quantum and classical mechanics and field theories, relativity and gravitation, statistical physics, thermodynamics, mathematical foundations of physical theories, etc. Preferred are papers using modern methods of functional analysis, probability theory, differential geometry, algebra and mathematical logic. Papers without direct connection with physics will not be accepted. Manuscripts should be concise, but possibly complete in presentation and discussion, to be comprehensible not only for mathematicians, but also for mathematically oriented theoretical physicists. All papers should describe original work and be written in English.