P-ADIC RATIONAL DYNAMIC SYSTEMS
Khamidov Sherali Shirinovich Teacher at Bukhara State Pedagogical Institute
Keywords:
Rational dynamical systems; fixed point; invariant set; Siegel disk; fields of p-adic complex numbers.Abstract
The work uses the methods of mathematical analysis, complex analysis and p-adic analysis. Study of the theory of dynamical systems with discrete time in the field of p-adic complex numbers and their implementation:
- Find fixed points of a/(x^2+1) - rational functions;
- study the dynamics corresponding to the characteristics of fixed and points, in particular when this point is unique;
- find periodic points in case of the absence of a fixed point and investigate the dynamics in accordance with the nature of these points;
The results of the work on the development of the theory of discrete dynamical systems for the class of p-adic rational functions. The practical significance of the results obtained is expressed in the fact that they can be used for the further development of telecommunications, digital analysis and cryptography. The results have theoretical character. They can be used in the study of related areas of mathematics, the dynamics of biological and physical systems.
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