From the ergodic hypothesis to the fractal picture of the world. The birth and understanding of a new paradigm
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Science is experiencing a revolution associated with the replacement of a “continuous” paradigm to fractal (discrete) in its foundation. The task of the monograph is to eliminate some gaps and inconsistencies from the reconstructed foundation. 1. In the area of the stochastic movement, the phase trajectory changes its topological nature, ceasing to be a line. This was not taken into account by the ergodic theory and theory of dynamic chaos (before the stage of computational experiment), whose results are reviewed in the book from this angle. 2. Fractals are born in irreversible systems and are not born in reversible. In evidence of the existence of an irreversible dynamic chaos in reversible systems --- Hopf, Krylov, Sinai --- the same error is found --- the branch of solving the solution of the equation symmetrical in time, which meets the faceted movement. 3. Fractals can occur in isolated systems, since the entropy of real systems is not a measure of mess. 4. Following Mandelbrot, "Father" fractals, it is generally accepted that the fractal dimension is more topological, while it is smaller than it. It follows that the fractals located in our three -dimensional space should have zero density, which is not observed, so real systems are only fractal -like, having a fractal structure in the final range of scale. This displays the principle of additional continuous (kinetic) and fractal descriptions that exclude each other in the field of irreversible processes. 5. The only exception is the universe, which, due to its infinity, may turn out to be a "real" fractal with zero density, which would mean a revision of the cosmological picture of the world. 6. The world is fractal, because this ensures the maximum speed of its evolution, which occurs with a decrease in the fractal dimension of the Universe.
Fractals penetrate today into a variety of scientific disciplines, so the book can be useful to a wide range of readers with sufficient physical and mathematical education
Fractals penetrate today into a variety of scientific disciplines, so the book can be useful to a wide range of readers with sufficient physical and mathematical education
Author:
Author:Хайтун С.Д.
Cover:
Cover:Soft
Category:
- Category:Comics and Graphic Novels
- Category:History & Geography
- Category:Reference books
- Category:Natural sciences
Publication language:
Publication Language:Russian
Paper:
Paper:printing
Age restrictions:
Age restrictions:16+
ISBN:
ISBN:978-5-9519-3631-8
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