On a topological closeness of perturbed Julia sets

In the present work we expand our previous work in [1] by introducing the Julia Deviation Distance and the Julia Deviation Plot in order to study the stability of the Julia sets of noise-perturbed Mandelbrot maps. We observe a power-law behaviour of the Julia Deviation Distance of the Julia sets of...

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Bibliographic Details
Published in:Applied mathematics and computation 2010-11, Vol.217 (6), p.2883-2890
Main Authors: Andreadis, Ioannis, Karakasidis, Theodoros E.
Format: Article
Language:English
Subjects:
Additive dynamic noise
Deviation
Distance
Dynamics
Exact sciences and technology
Global analysis, analysis on manifolds
Julia set
Mandelbrot map
Mathematical analysis
Mathematical models
Mathematics
Noise
Noise levels
Numerical analysis
Numerical analysis. Scientific computation
Sciences and techniques of general use
Stability
Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds
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Summary:In the present work we expand our previous work in [1] by introducing the Julia Deviation Distance and the Julia Deviation Plot in order to study the stability of the Julia sets of noise-perturbed Mandelbrot maps. We observe a power-law behaviour of the Julia Deviation Distance of the Julia sets of a family of additive dynamic noise Mandelbrot maps from the Julia set of the Mandelbrot map as a function of the noise level. Additionally, using the above tools, we support the invariance of the Julia set of a noise-perturbed Mandelbrot map under different noise realizations.
ISSN:0096-3003
1873-5649
DOI:10.1016/j.amc.2010.08.024