Research on fractal structure of generalized M--J sets utilized Lyapunov exponents and periodic scanning techniques

DOI10.1016/j.amc.2005.08.015zbMath1102.37031OpenAlexW1968468087MaRDI QIDQ2493683

Pei-Jun Chang, Xing-Yuan Wang

Publication date: 16 June 2006

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.amc.2005.08.015

zbMATH Keywords

Lyapunov exponentfractalgeneralized Mandelbrot-Julia setsphysical meaningdiscontinuity evolution lawperiodic scanningtopological inflexibility

Mathematics Subject Classification ID

Related Items (23)

Application of Fixed Point Iterative Methods to Construct Fractals and Anti-fractals ⋮ Additive perturbed generalized Mandelbrot-Julia sets ⋮ A brief note on fractal dynamics of fractional Mandelbrot sets ⋮ The generalized M-J sets for bicomplex numbers ⋮ Generalized Mandelbrot sets of a family of polynomials \(P_n(z)= z^n+z+c\); \((n \geq 2)\) ⋮ The Julia sets of Chebyshev's method with small degrees ⋮ Control of Julia Sets in Generalized Alternated System ⋮ Control and synchronization of Mandelbrot sets in coupled map lattice ⋮ CONTROL AND SYNCHRONIZATION OF JULIA SETS GENERATED BY A CLASS OF COMPLEX TIME-DELAY RATIONAL MAP ⋮ Quasi-sine Fibonacci M set with perturbation ⋮ A SHORT NOTE ON THE BOUNDEDNESS ANALYSIS AND CONTROL OF THE SPATIAL FRACTAL SET FROM A KIND OF CHAIN COUPLING LOGISTIC TYPE MAP ⋮ Accurate computation of periodic regions' centers in the general \(M\)-set with integer index number ⋮ Control of the thermal fractal diffusion of tightly compressed heterogeneous layers of thin plates ⋮ On numerical approximations of the area of the generalized Mandelbrot sets ⋮ Noise perturbed generalized Mandelbrot sets ⋮ Julia sets and Mandelbrot sets in Noor orbit ⋮ The generalized Julia set perturbed by composing additive and multiplicative noises ⋮ RENDERING OF THE INSIDE STRUCTURE OF THE GENERALIZED M SET PERIOD BULBS BASED ON THE PRE-PERIOD ⋮ Bivariate Newton-Raphson method and toroidal attraction basins ⋮ Recurrence analysis on Julia sets of semigroups of complex polynomials ⋮ Control and synchronization of Julia sets of the complex dissipative standard system ⋮ The generalized Mandelbrot set perturbed by composing noise of additive and multiplicative ⋮ Generalized Julia set in coupled map lattice and its coupling and synchronization

Cites Work

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• The generalized Mandelbrot-Julia sets from a class of complex exponential map
• Switched processes generalized Mandelbrot sets for complex index number
• Physical meaning for Mandelbrot and Julia sets
• ANALYSIS OF C-PLANE FRACTAL IMAGES FROM z ← z^α + c FOR (α < 0)

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