N. V. STEPANOV AND HIS GEOMETRIC THEORY OF ORDINARY DIFFERENTIAL EQUATIONS

G. A. Banaru

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N. V. STEPANOV AND HIS GEOMETRIC THEORY OF ORDINARY DIFFERENTIAL EQUATIONS

机译：N. V. STEPANOV和他的常微分方程的几何理论

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We review the main results of the geometric theory of ordinary differential equations obtained by the prominent Russian geometer N. V. Stepanov (1926-1991). Some results obtained by Stepanov are illustrated by examples of third- and five-order equations.

机译：我们回顾了由著名的俄罗斯几何学家N. V. Stepanov（1926-1991）获得的常微分方程几何理论的主要结果。 Stepanov获得的一些结果通过三阶和五阶方程的示例进行了说明。

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来源
《Journal of Mathematical Sciences》 |2019年第3期|245-250|共6页
作者
G. A. Banaru;
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作者单位

Smolensk State University, Smolensk, Russia;

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原文格式 PDF
正文语种 eng
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关键词
ordinary differential equation; invariant; connection; classification; differential-algebraic characteristics; symmetry group;

机译：常微分方程;不变;联系;分类;差分代数特征;对称组;

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专利

1. N. V. STEPANOV AND HIS GEOMETRIC THEORY OF ORDINARY DIFFERENTIAL EQUATIONS [J] . G. A. Banaru Journal of Mathematical Sciences . 2019,第3期

机译：N.V.Tepeanov及其对普通微分方程的几何理论
2. Geometric Theory of Differential Systems: Linearization Criterion for Systems of Second-Order Ordinary Differential Equations with a 4-Dimensional Solvable Symmetry Group of the Lie-Petrov Type VI_1 [J] . A. V. Aminova, N. A.-M Aminov Journal of Mathematical Sciences . 2009,第2期

机译：微分系统的几何理论：具有Lie-Petrov类型VI_1的4维可解对称群的二阶常微分方程组的线性化准则
3. ON THE NONEXISTENCE OF PURELY STEPANOV ALMOST-PERIODIC SOLUTIONS OF ORDINARY DIFFERENTIAL EQUATIONS [J] . JAN ANDRES, DENIS PENNEQUIN Proceedings of the American Mathematical Society . 2012,第8期

机译：关于常微分方程的纯Stepanov概周期解的不存在性
4. THE RIEMANN AND EINSTEIN-WEYL GEOMETRIES IN THE THEORY OF ORDINARY DIFFERENTIAL EQUATIONS, THEIR APPLICATIONS AND ALL THAT [C] . Valerii Dryuma NATO Advanced Research Workshop on New Trends in Integrability and Partial Sovability . 2004

机译：普通微分方程理论中的riemann和爱因斯坦 - Weyl几何形状，它们的应用和所有
5. Geometric field stability and normal field curvature of solution sets of ordinary differential equations in two variables. [D] . Kerns, Leslie L. 2006

机译：具有两个变量的常微分方程解集的几何场稳定性和法向曲率。
6. The Picard-Vessiot Theory of Homogeneous Linear Ordinary Differential Equations [O] . E. R. Kolchin 1946

机译：齐次线性常微分方程的Picard-Vessiot理论
7. Geometrical methods in the theory of ordinary differential equations V. I. Arnold, 2nd ed., Springer, 1988, 351 pp. [O] . Rota Gian-Carlo 1990

机译：常微分方程理论中的几何方法V. I. Arnold，第二版，Springer，1988，351 pp。
8. Schroedinger Equation for Central Power Law Potentials and the Classical Theory of Ordinary Linear Differential Equations of the Second Order [R] . Lima, M. L., Mignaco, J. A. 1985

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N. V. STEPANOV AND HIS GEOMETRIC THEORY OF ORDINARY DIFFERENTIAL EQUATIONS

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