On the Second-Degree Homogeneous Differential System's Exclusive Directions

Authors

  • Khusanov Bozorboy Candidate of Physical and Mathematical Sciences, Samarkand State Institute of Architecture and Civil Engineering, Uzbekistan
  • Kulmirzaeva Gulrabo Abduganiyevna Senior teacher of Samarkand State Institute of Architecture and Civil Engineering, Uzbekistan

Keywords:

polynomial vector-function, vector norm, equator, manifold, isolated, saddle

Abstract

In the article we study the case of coexistence of exceptional directions of the system.

dx/dt=X^2 (x), x = (x1 , x2 , x3),

Here Х2(х) – is homogeneous polynomial vector is a function of degree 2, and X_3^2(x) has a factor х3 .

References

Sharipov Sh.R. "Classification of integral manifolds of a homogeneous three-dimensional system according to the structure of limit sets" Diff. equations, T.VII. 1971. No. 3. pp. 461 – 470.

Khaimov N.B. Some theorems on singular points of the first group. Uch. Zap. Stalinabdsky pedins-that vol. I, 1952 pp. 45 - 113

Khusanov B., Sharipov Sh.R. Mamashev S.Kh. "On some questions of the trajectory of an n-dimensional generalized homogeneous differential system". Ed. AZh KazSSR. Series of physical and mathematical sciences, 1981, No. 3. pp 33 – 43.

Sharipov Sh.R. "On the behavior of integral curves of a system of n - equations at infinity" Scientific works. Departments of higher mathematics. MKI. 1968, pp. 103-127.

Poincare A. "On curves defined by differential equations". M - L. GTTI. 1947 – 390 pages

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Published

2022-03-24

How to Cite

Bozorboy, K. ., & Abduganiyevna, K. G. . (2022). On the Second-Degree Homogeneous Differential System’s Exclusive Directions. European Multidisciplinary Journal of Modern Science, 4, 389–393. Retrieved from https://emjms.academicjournal.io/index.php/emjms/article/view/102

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