منابع مشابه
Dynamics of Mandelbrot Cascades
Mandelbrot multiplicative cascades provide a construction of a dynamical system on a set of probability measures defined by inequalities on moments. To be more specific, beyond the first iteration, the trajectories take values in the set of fixed points of smoothing transformations (i.e., some generalized stable laws). Studying this system leads to a central limit theorem and to its functional ...
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We consider here the interaction of direct and inverse cascades in a hierarchical nonlinear system that is continuously loaded by external forces. The load is applied to the largest element and is transferred down the hierarchy to consecutively smaller elements, thereby forming a direct cascade. The elements of the system fail (i. e., break down) under the load. The smallest elements fail first...
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The Mandelbrot set is an extremely well-known mathematical object that can be described in a quite simple way but has very interesting and non-trivial properties. This paper surveys some results that are known concerning the (non-)computability of the set. It considers two models of decidability over the reals (which are treated much more thoroughly and technically in [1], [2], [3] and [4] amon...
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Xue-Zao Ren, Zimo Yang, Bing-Hong Wang, and Tao Zhou School of Science, Southwest University of Science and Technology, Mianyang 621010, People’s Republic of China Web Sciences Center, University of Electronic Science and Technology of China, Chengdu 610054, People’s Republic of China Department of Modern Physics, University of Science and Technology of China, Hefei 230026, People’s Republic of...
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By means of a graphical journey across the Mandelbrot set for the classic quadratic iterator f (z) : z 2 + q, we illustrate how connectivity breaks as the seed z 0 is no longer at the critical point of f (z). Finally we suggest an attack to the MLC conjecture.
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ژورنال
عنوان ژورنال: Communications in Mathematical Physics
سال: 2013
ISSN: 0010-3616,1432-0916
DOI: 10.1007/s00220-013-1829-4