منابع مشابه
The Influence of Benoît B . Mandelbrot on Mathematics
Introduction We begin this article, which deals largely with Benoît B. Mandelbrot’s contributions to and influence upon mathematics, with a quotation from the introduction to Fractals: Form, Chance, and Dimension [16]. This essay, together with many pictures and numerous lectures in the same vein, changed the way science looks at nature and had a significant impact on mathematics. It is easy fo...
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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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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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ژورنال
عنوان ژورنال: Nature
سال: 2010
ISSN: 0028-0836,1476-4687
DOI: 10.1038/468378a