Differential-geometric structure and spectral properties of nonlinear completely integrable dynamical systems of the Mel'nikov type

1990 ◽  
Vol 42 (5) ◽  
pp. 579-583 ◽  
Author(s):  
V. G. Samoilenko
Keyword(s):  
Dynamical Systems ◽  
Geometric Structure ◽  
Spectral Properties ◽  
Completely Integrable ◽  
Integrable Dynamical Systems

SINGULAR FOLIATION GENERATED BY AN ORBIT OF FAMILY OF VECTOR FIELDS

2021 ◽  
Vol 10 (4) ◽  
pp. 2141-2147
Author(s):  
X.F. Sharipov ◽  
B. Boymatov ◽  
N. Abriyev
Keyword(s):  
Dynamical Systems ◽  
Euclidean Space ◽  
Control Theory ◽  
Vector Fields ◽  
Singular Foliation ◽  
Completely Integrable ◽  
Conformal Vector ◽  
Conformal Vector Fields ◽  
Systems Control

Geometry of orbit is a subject of many investigations because it has important role in many branches of mathematics such as dynamical systems, control theory. In this paper it is studied geometry of orbits of conformal vector fields. It is shown that orbits of conformal vector fields are integral submanifolds of completely integrable distributions. Also for Euclidean space it is proven that if all orbits have the same dimension they are closed subsets.

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