منابع مشابه
Fractal Newton Basins
The dynamics of complex cubic polynomials have been studied extensively in the recent years. The main interest in this work is to focus on the Julia sets in the dynamical plane, and then is consecrated to the study of several topics in more detail. Newton’s method is considered since it is the main tool for finding solutions to equations, which leads to some fantastic images when it is applied ...
متن کاملModels of Fractal River Basins
Experimental analyses of river networks(1) have shown clear examples of behavior analogous to critical phenomena characterized by the absence of a single well-defined length scale reflected in a power-law behavior of various quantities. A fundamental question that arises from these observations is whether, in analogy with conventional critical phenomena, one may fruitfully classify this behavio...
متن کاملBasins of Newton Maps and Asymptotic Values
Newton’s root finding method applied to a (transcendental) entire function f : C → C is the iteration of a meromorphic function Nf . It is well known that if for some starting value z0, Newton’s method converges to a point ξ ∈ C, then f has a root at ξ. We show that in many cases, if an orbit converges to ξ = ∞ for Newton’s method, then f has a ‘virtual root’ at ∞. More precisely, we show that ...
متن کاملCatastrophic bifurcation from riddled to fractal basins.
Most existing works on riddling assume that the underlying dynamical system possesses an invariant subspace that usually results from a symmetry. In realistic applications of chaotic systems, however, there exists no perfect symmetry. The aim of this paper is to examine the consequences of symmetry-breaking on riddling. In particular, we consider smooth deterministic perturbations that destroy ...
متن کاملFractal analysis of drainage basins on Mars
[1] We used statistical properties of drainage networks on Mars as a measure of martian landscape morphology and an indicator of landscape evolution processes. We utilize the Mars Orbiter Laser Altimeter (MOLA) data to construct digital elevation maps (DEMs) of several, mostly ancient, martian terrains. Drainage basins and channel networks are computationally extracted from DEMs and their struc...
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ژورنال
عنوان ژورنال: Discrete Dynamics in Nature and Society
سال: 2006
ISSN: 1026-0226,1607-887X
DOI: 10.1155/ddns/2006/28756