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AN ANALYTICAL DESCRIPTION OF THE MANDELBROT SET FOR THE SOME TWO DIMENSIONAL MAPPINGS
Maqola haqida umumiy ma'lumotlar
In this paper proposes one of generalizations ofthe following the mappings to the multi-dimensional case. An analytical description of the Mandelbrot set for the twodimensional case is obtained. The properties of Julia sets are studied.
- Sharkovsky, A. N. “Coexistence of Cycles of a Continuous Map of a Line into itself.” // Ukrain. Mat. Z 16 (1964), 61-71 (In Russian).
- B. L. Van-der-Varden. Algebra. // M.: Mir, 1976. p-648
- Devaney, R. L. A first course in chaotic dynamical systems. New York: Westview Press, 1992. p-321.
- Devaney, R. L. An Introduction to Chaotic Dynamical Systems. New York: Westview Press, 1989. p-181.
- Fatou, P. Sur les Equationes Fonctionelles. // Bull. Soc. Math. France 48 (1920), 33-94, 208-314.
- Feigenbaum, M.J. Qualitative Universality for a Class of Nonlinear Transformations. //J. Stat. Phys. 19 (1978), 25-52.
- Julia, G. Memoire sur l’Iteration des Fonctions Rationelles // J. Math Pures Appl. 4 (1918). 47-245.
- Li, T., and Yorke, J. Period Three imply Chaos //American Mathematical Monthly 82 (1975), 985-992.
- Mandelbrot, B. Fractals Aspects of the Iteration of . Nonlinear dynamics, Annals of the New York Academy of science 357 (1980), 249-252.
- Richard, A.H. A first Course in Discrete Dynamical Systems // Springer-Verlag. 1994. P-225.
Seytov, S. J., & Oxunova, M. O. (2023). AN ANALYTICAL DESCRIPTION OF THE MANDELBROT SET FOR THE SOME TWO DIMENSIONAL MAPPINGS. Academic Research in Educational Sciences, 4(12), 156–169. https://doi.org/
Seytov, Shavkat, and Muxlisaxon Oxunova,. “AN ANALYTICAL DESCRIPTION OF THE MANDELBROT SET FOR THE SOME TWO DIMENSIONAL MAPPINGS.” Academic Research in Educational Sciences, vol. 12, no. 4, 2023, pp. 156–169, https://doi.org/.
Seytov, J. and Oxunova, O. 2023. AN ANALYTICAL DESCRIPTION OF THE MANDELBROT SET FOR THE SOME TWO DIMENSIONAL MAPPINGS. Academic Research in Educational Sciences. 12(4), pp.156–169.