Ikki o’lchamli ko’pxilliklarda dinamik sistema

Область применения: Каршинский государственный университет, высшие учебные заведения.

"Dynamic system in two-dimensional manifolds"

master's thesis on the subject
ANNOTATION
Key words: This master's thesis is devoted to the study of dynamic systems in two-dimensional manifolds. In many years, it will consist of studying dynamic system, geometry of orbits of vector fields, theory of dynamic systems, mechanics, theory of optimal control, geometry of differentiable solutions.
Research objects: Karshi State University.
The purpose of the work: It is intended to study the geometry and topology of the dynamic system defined in the multiplicity.
Research methods: comparative analysis formalization, analysis, synthesis, observation, experiment, scientific abstraction, analytical method.
The results obtained and their novelty:
- It is shown that the orbit of a dynamic system lies in a string;
- It is proved that the orbit lying on the string consists of a line homeomorphic to the circle when the parameter change is rational;
- It is proved that the orbit lying on the string consists of a line homeomorphic to a straight line when the parameter change is irrational.
Practical significance: the geometry and topology of layered manifolds formed by dynamic systems is one of the fundamental researches conducted in the field of geometry and topology in our country, and the results obtained in the master's thesis serve this direction. The study of this field has wide applications in fields such as dynamic systems, optimal control theory.
The level of application and economic efficiency: the conclusions and suggestions made in the research process are recommended to be used in the training process of the personnel being trained at the Department of Algebra and Geometry of Karshi State University. The materials of the dissertation are used to improve and teach the curriculum of analytic geometry, topology, algebra and number theory at Karshi State University.
Field of application: Karshi State University, higher educational institutions.