TWO LECTURES ABOUT THE TWO WAYS OF SYMMETRY INVESTIGATION


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Trubetskov D. I. TWO LECTURES ABOUT THE TWO WAYS OF SYMMETRY INVESTIGATION. Izvestiya VUZ, Applied Nonlinear Dynamics, 2013, vol. 21, iss. 4, pp. 13-33 DOI: 10.18500/0869-6632-2013-21-4-13-33


These lectures were delivered to the high school students at the School – seminar «Nonlinear Days for Youth in Saratov – 2012» in October 2012. They present the two ways of historical investigation of symmetry. The first way is self-similarity, i.e. invariance at dimension scale changing. In a more general way the term «scaling» is used, meaning the existence of power-law correlation between some variable and variables x1, ...xn: y = Axα1...xαn1 (self-similarity) appearing in various fields of science and culture. G.I. Barenblatt indicates that scaling laws never appear by accident. They always reveal the most important property of the phenomenon under consideration: its self-similarity. The term self-similarity means that changing in time and space, a phenomenon repeats itself in changed temporary and / or space scales. Lecture 2 describes the second way of symmetry investigation. It is search for solutions of algebraic equations which led to creation of group theory. As a background the lecture includes historical events and characters dealing with the described scientific investigations.

DOI: 
10.18500/0869-6632-2013-21-4-13-33
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BibTeX

@article{Трубецков-IzvVUZ_AND-21-4-13,
author = {Dmitry Ivanovich Trubetskov},
title = {TWO LECTURES ABOUT THE TWO WAYS OF SYMMETRY INVESTIGATION},
year = {2013},
journal = {Izvestiya VUZ. Applied Nonlinear Dynamics},
volume = {21},number = {4},
url = {http://andjournal.sgu.ru/en/articles/two-lectures-about-the-two-ways-of-symmetry-investigation},
address = {Саратов},
language = {russian},
doi = {10.18500/0869-6632-2013-21-4-13-33},pages = {13--33},issn = {0869-6632},
keywords = {Symmetry,self-similarity,scaling,fractals,power series,similarity,golden and silver ratio,chaos.},
abstract = {These lectures were delivered to the high school students at the School – seminar «Nonlinear Days for Youth in Saratov – 2012» in October 2012. They present the two ways of historical investigation of symmetry. The first way is self-similarity, i.e. invariance at dimension scale changing. In a more general way the term «scaling» is used, meaning the existence of power-law correlation between some variable and variables x1, ...xn: y = Axα1...xαn1 (self-similarity) appearing in various fields of science and culture. G.I. Barenblatt indicates that scaling laws never appear by accident. They always reveal the most important property of the phenomenon under consideration: its self-similarity. The term self-similarity means that changing in time and space, a phenomenon repeats itself in changed temporary and / or space scales. Lecture 2 describes the second way of symmetry investigation. It is search for solutions of algebraic equations which led to creation of group theory. As a background the lecture includes historical events and characters dealing with the described scientific investigations. }}