Affiliation:
1. Shenyang Ligong University
Abstract
In this paper, the chaotic orbit in Mandelbrot set is introduced. On the basis of other scholars research, the character and distribution rules of pre-periodic orbits and pre-periodic points-Misiurewiz points about Mandelbrot set chaos-fractal images were studied. The software of constructing the general M-J set with Java Applet is improved. Using the method of computer mathematic experiments, the paper analyses the fixed orbit and period orbit in the M-set, gains the topology relationship of M set in super stable points, a recurrence formula between the period orbit and M-set periodic-buds is created.
Publisher
Trans Tech Publications, Ltd.
Reference6 articles.
1. David Arroyo, Gonzalo Alvarez. Application of Gray codes to the study of the theory of symbolic dynamics of unimodal maps. Communications in Nonlinear Science and Numerical Simulation, In Press, Corrected Proof, Available online 20 November (2013).
2. Ioannis Andreadis, Theodoros E. Karakasidis. On numerical approximations of the area of the generalized Mandelbrot sets[J]. Applied Mathematics and Computation, Volume 219, Issue 23, 1 August 2013, Pages 10974-10982.
3. ZHU Wei-Yong. etc. A Series Conjectures of M-J Chaos-Fractal Image Construction by the Periodic Buds Fibonacci Sequence[J]. Chinese Journal Computer. 2003 Vol. 26 No. 2 221~226.
4. Ravenel D C. Complex Cobordism and Stable Homotopy Groups of Spheres (Second edition) [M]. Providence: AMS Chelsea Publishing, 2004. 66~69.
5. YUAN Zheng-Xiong, Huang Guo-He. Chaos-based encryption for fractal image coding[J]. Chinese Physics B. 2012, Vol. 21, No. 1, 010502-1~010502-12.