ISSN 0869-6632 (Print)
ISSN 2542-1905 (Online)

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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

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Two lectures about the two ways of symmetry investigation

Trubetskov Dmitriy Ivanovich, Saratov State University

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 = Ax1α1...xnαn, where A, α1,...αn – are constant. Lecture 1 gives examples of scaling (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.

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