The Exploration of Two-Dimensional Cases of Feigenbaum’s Results
The Exploration of Two-Dimensional Cases of Feigenbaum’s Results
Keywords:
Keywords: Mandelbrot set, Julia set, bifurcation, fixed point, periodic point.Abstract
The focus of this paper is on exploring the multi-dimensional case of the results of M.Feigenbaum. Specifically, we delve into the properties of Julia and Mandelbrot sets in the context of the renowned mapping from the plane to itself in two dimensions. These sets play a crucial role in determining the asymptotic behavior of trajectories for certain mappings. The primary outcomes of this investigation include the analytical solutions derived for locating fixed and periodic points. Additionally, the paper presents computational simulations aimed at describing Julia and Mandelbrot sets.
References
Seytov, S.J., Eshmamatova, D.B. , Discrete Dynamical Systems of Lotka–Volterra and Their Applications on the Modeling of the Biogen Cycle in Ecosystem. Lobachevskii Journal of Mathematics., 2023, 44(4), pp. 1471–1485.
Eshmamatova, D.B., Seytov, S.J., Narziev, N.B. Basins of Fixed Points for Composition of the Lotka– Volterra Mappings and Their Classification. Lobachevskii Journal of Mathematics, 2023, 44(2), pp. 558– 569
