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Fractal Structure of Logistic Complex Dynamics

Author: GuoJing
Tutor: ShengZhongPing
School: Northeast Normal University
Course: Computational Mathematics
Keywords: Cycle Orbit Super Attraction Fixed Point Logistic Map Lyapunov Index Surface Mandelbrot Set Branch
CLC: O19
Type: Master's thesis
Year: 2013
Downloads: 17
Quote: 0
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Abstract


Logistic map of complex branching structure is discussed in this paper.First of all, the basic background, basic concept and two propositions of fractal dynamic system are given.The counter example which is the complex iterative p cycle track of second derivative isn’t equal is illustrated.So it isn’t a second-order characteristic.General power system is introduced the classification of cycle track.At the same time, this paper gives the portrait of super attracting fixed point.The length of the simplified system is given and the argument of iteration is given.This paper determines the attracting basin radius of the super attract fixed point.It gives necessary and sufficient condition which the simplified system initial argument after n step m circle back to the original argument.It provides a theoretical basis for depicting attract fixed point.Branch structure of the Logistic system is discussed, and appeals to the fixed point and is provided by two parameters theorem of periodic orbits.We draw the figure with the Mandelbrot set of branch of the Logistic system.This paper expounds any r belongs to Logistic mapping the Mandelbrot set and the length of r is less than4and4is the supremum. At last,we review the result which Professor Zhongping Sheng gives Lyaponov index surface of Logistic system,and draws the curve surface of Lyapunov index, and expounds the relationship between the curved surface of Lyapunov index and the Mandelbrot set.It improves and enrichs fractal structure theory of complex dynamic system.

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CLC: > Mathematical sciences and chemical > Mathematics > Dynamical systems theory
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