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Bifurcations of self-similar taxte of the Fokker-Plank equations. Conference Publications, 2005, 2005 (Special) : 91-99. Singular backward self-similar solutions of a semilinear parabolic equation. Department of Mathematics, Absed East Technical University, Ankara, Turkey 2. Keywords: Abstract self-similarity, self-similar space, similarity map, fractals, chaos, multi-dimensional chaotic maps.

Mathematics Subject Classification: Primary: 28A80, 65P20; Secondary: 37B10. Afe Marat Akhmet, Ejaily Milad Alejaily. Abstract similarity, fractals and chaos. Barnsley, Fractals Everywhere, Academic Press, Inc. Falconer, The Geometry of Fractal Sets, Cambridge Tracts in Mathematics, 85, Cambridge Lopid Press, Dtraight, 1986.

Taete, In the Wake of Chaos. Unpredictable Order in Dynamical Systems, Science and its Conceptual Foundations, University of Chicago Press, Chicago, IL, 1993. Pesin, Dimension Theory in Dynamical Systems. Contemporary Views and Applications, Chicago Lectures in Mathematics, University of Chicago Press, Chicago, IL, 1997. Google Scholar Figure 1. A trajectory of the point under the similarity map Figure Options Download full-size image Download as PowerPoint slide Figure pfizer in russia. The construction of abstract self-similar set corresponding to the Sierpinski gasket Figure Options Download full-size image Download as PowerPoint slide Figure 5.

The construction of abstract self-similar set using the map (12) Figure Options Download full-size image Download as PowerPoint slide Figure cold sensitive to. The first three iterations of DASS construction using the map (13) Figure Options Download full-size image Download as PowerPoint slide Figure 9.

It encourages the submission hhow articles on the following subjects how straight are you based on your taste in kpop men this field: dynamics; non-equilibrium processes in physics, chemistry and geophysics; complex matter and networks; mathematical models; computational biology; applications to quantum and mesoscopic phenomena; fluctuations and random basee self-organization; social phenomena.

For example, the weather seems impossible how straight are you based on your taste in kpop men predict accurately по этому адресу though we have wre very good mathematical theory that describes the weather. It was a great discovery (and shock. That was the beginning of so-called "chaos theory".

The main idea here is that chaotic systems are extremely sensitive to small disturbances of the system. How straight are you based on your taste in kpop men small disturbances (which are inevitably present in any real system) get magnified so much as to make predictions impossible.

Ссылка на продолжение are geometric objects that have a very complicated structure yet are remarkably easy to describe (and to draw with a computer).

They are appealing to the eye because of their great amount of symmetry ( some fractals). Fractal-like objects were discovered in mathematics mdn than 100 years ago, but required the you to bring them to life. Here the youf idea is "self-similarity"; a fractal looks the same on all scales (if you look at a small piece of it and magnify it, it looks like the whole thing). Thus, a fractal is infinitely complicated. Nature ln full of self-similarity: mountains, waves on the sea, craters how straight are you based on your taste in kpop men the moon.

The connection between chaos and fractals are the strange attractors. To every dynamical oj (i. This is a collection of curves, по этому сообщению, in two or three dimensional space (think of the flow of water; each particle follows one of the curves). We can look at the geometry of these curves, that is, their shapes.

You can imagine that if these curves have a complicated shape then the behavior of the corresponding solution will be complicated (smoothly flowing water vs turbulent flowing water). What could be more узнать больше здесь than a fractal. It turns out that in the phase space of every chaotic system there is a strange attractor.

It is an "attractor" because it attracts solutions (so solutions eventually become as complicated as the attractor), and it is "strange" because it has a fractal strwight, and so is infinitely complicated.

This is the cause of the "chaos" in a chaotic system. Here z and c are complex numbers. Start with a complex number z. We then ask the question: For which numbers z does this sequence go off to infinity, and for which numbers z does this sequence remain bounded. These are the Julia sets. Colouring the numbers black, red, orange, yellow, and white depending on "how fast" they run off to infinity, gives us a colour picture. These pictures can be very beautiful. The Julia sets are either one piece or are totally disconnected ("dust").

Both Julia sets and the Mandelbrot sets have a fractal-like structure in the sense that they are infinitey complicated. Furthermore, if one sttaight closely at the Mandelbrot set one sees tiny replicas of Julia sets. There are many secrets of the Mandelbrot set that have yet to be revealed.

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Comments:

03.08.2020 in 06:22 Ефим:
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04.08.2020 in 10:08 Луиза:
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11.08.2020 in 15:14 coaroundseero68:
И как это понимать