自由系统与辛Haantjes结构的可积性定理

IF 0.5 Q4 PHYSICS, MATHEMATICAL Journal of Geometry and Symmetry in Physics Pub Date : 2022-01-01 DOI:10.7546/jgsp-63-2022-39-64

K. Kikuchi, Tsukasa Takeuchi

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引用次数: 0

摘要

Ikeda和Sakamoto研究了完整动力系统的线性第一积分的动态控制问题，我们的命题证明了与他们在可积性上相同的结果。此外，Tempesta和Tondo还定义了一个辛Haantjes流形，它是利用$(1,1)$张量场对可积系统的表征。从几何的角度，利用辛汉杰流形的具体构造证明了动态控制问题的可积性。

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Integrability Theorems of Free Systems and Symplectic Haantjes Structures

Ikeda and Sakamoto studied a dynamical control problem called the linear first integral for holonomic dynamical systems, and our proposition proved the same result as theirs in integrability. % Also, a symplectic Haantjes manifolds has been defined by Tempesta and Tondo, which is a characterization of integrable systems using $(1,1)$ tensor fields. We show integrability in dynamical control problems from a geometric point of view by means of a concrete construction of a symplectic Haantjes manifold.

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来源期刊

Journal of Geometry and Symmetry in Physics PHYSICS, MATHEMATICAL-

CiteScore

1.50

自引率

25.00%

发文量

期刊介绍： The Journal of Geometry and Symmetry in Physics is a fully-refereed, independent international journal. It aims to facilitate the rapid dissemination, at low cost, of original research articles reporting interesting and potentially important ideas, and invited review articles providing background, perspectives, and useful sources of reference material. In addition to such contributions, the journal welcomes extended versions of talks in the area of geometry of classical and quantum systems delivered at the annual conferences on Geometry, Integrability and Quantization in Bulgaria. An overall idea is to provide a forum for an exchange of information, ideas and inspiration and further development of the international collaboration. The potential authors are kindly invited to submit their papers for consideraion in this Journal either to one of the Associate Editors listed below or to someone of the Editors of the Proceedings series whose expertise covers the research topic, and with whom the author can communicate effectively, or directly to the JGSP Editorial Office at the address given below. More details regarding submission of papers can be found by clicking on "Notes for Authors" button above. The publication program foresees four quarterly issues per year of approximately 128 pages each.

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