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Evolutionary Differential Based on Poincaré Section

Ali Sanayei

Abstract



Most mathematicians believe that the primary target in differential equations is studying the transformation of the median universe, and nothing except "transformation" is constant. [1] Has this target practically resulted? Are classical differential equations (raised by Newton and Leibniz) fully efficient to recognize and review the natural systems? "Differential" means comparative transformation, comparative transformation means motion, and motion means evolution. Evolution means creation of information to get more adaptable. Classical differential in not defined in discrete, whereas the creation of information occurs in discrete. Whatever is placed in Nature's essence is uncertainty, and uncertainty is an attribute of information [2,3], not matter and energy. For reviewing the natural systems in this paper, evolutionary differential based on Poincaré section [type one] has been replaced instead of the classical differential and we have stated some practical examples with their results.

Keywords


System, holism, self-organization, information, interaction, evolution, differential, iterative maps, fractal dimension, uncertainty, Poincaré section, A.S. method, A.S. diagram.

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