任意奇阶可积保守耗散系统的新情形

IF 0.6 4区数学 Q3 MATHEMATICS

Doklady Mathematics Pub Date : 2025-10-17 DOI:10.1134/S1064562424602129

M. V. Shamolin

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引用次数: 0

摘要

我们给出了任意奇阶可积动力系统的新情况，这些系统的某些变量是齐次的，并且可以区分偶数维流形的余切束上的系统。在这种情况下，力场（系统中的移位发生器）分为内部（保守）和外部（具有不同符号的耗散）。外部域是通过一些单模变换引入的，并推广了之前考虑的域。给出了第一积分和不变微分形式的完备集。

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New Cases of Integrable Conservative and Dissipative Systems of Any Odd Order

We present new cases of integrable dynamical systems of any odd order that are homogeneous in terms of some of their variables and in which a system on the cotangent bundle of an even-dimensional manifold can be distinguished. In this case, the force field (shift generator in the system) 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 generalizes previously considered fields. Complete sets of both first integrals and invariant differential forms are given.

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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 It publishes brief scientific reports on previously unpublished significant new research in mathematics and its applications.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.