New Cases of Integrable Ninth-Order Conservative and Dissipative Dynamical Systems

IF 0.5 4区数学 Q3 MATHEMATICS

Doklady Mathematics Pub Date : 2024-09-13 DOI:10.1134/s1064562424601434

M. V. Shamolin

引用次数: 0

Abstract

New cases of integrable ninth-order dynamical systems that are homogeneous in terms of some of their variables are presented, in which a system on the tangent bundle of a four-dimensional manifold can be distinguished. In this case, the force field is divided into an internal (conservative) and an external one, which has dissipation of different signs. The external field is introduced using some unimodular transformation, and it generalizes previously considered fields. Complete sets of both first integrals and invariant differential forms are given.

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可积分九阶保守和耗散动力系统的新案例

摘要介绍了可积分九阶动力系统的新情况，这些系统的某些变量是同质的，其中可以区分四维流形切线束上的系统。在这种情况下，力场分为内部力场（保守力场）和外部力场，后者具有不同符号的耗散。外部力场是通过某种单模态变换引入的，它概括了之前考虑过的力场。给出了第一积分和不变微分形式的完整集合。

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

Doklady Mathematics 数学-数学

CiteScore

1.00

自引率

16.70%

发文量

审稿时长

3-6 weeks

期刊介绍： Doklady Mathematics is a journal of the Presidium of the Russian Academy of Sciences. It contains English translations of papers published in Doklady Akademii Nauk (Proceedings of the Russian Academy of Sciences), which was founded in 1933 and is published 36 times a year. Doklady Mathematics includes the materials from the following areas: mathematics, mathematical physics, computer science, control theory, and computers. It publishes brief scientific reports on previously unpublished significant new research in mathematics and its applications. The main contributors to the journal are Members of the RAS, Corresponding Members of the RAS, and scientists from the former Soviet Union and other foreign countries. Among the contributors are the outstanding Russian mathematicians.