History of the School

The scientists of the school are concerned with the development of mathematical tools of fractal structures of dynamic systems and mesostructures that are non-equilibrium systems. The school emerged in the late 1980s when it branched off from the school of the geometric theory of functions and the qualitative theory of differential equations proposed by Academician M. A. Lavrentyev together with Prof. V. N. Monakhov, Corresponding Member of the USSR Academy of Science and Prof. P. P. Belinsky. The school was created at the NSTU department of higher mathematics in close co-operation with the Institute of Mathematics of the Siberian Branch of the Russian Academy of Sciences. Members of the school took an active part in the work of the city intercollegiate scientific seminar “Fractal structures and dynamic systems” under the direction of Prof. V. A. Seleznev, head of the department.

Currently the core of the school is formed by a group of mathematicians, mechanics and physicists interested in the theory and simulation of fractal structures in dynamic systems and general iteration processes, fundamentals of computational and computer geometry and dynamic flows in infomedia. The list of these researchers includes such competent and qualified specialists as Prof. V. V. Aseev, D. Sc. (Phys. & Math.), Prof. V. P. Golubyatnikov, D. Sc. (Phys. & Math.), Prof. V. I. Kruglikov, D. Sc. (Phys. & Math.), Prof. D. L. Tkachev, D. Sc. (Phys. & Math.), and others.

At the moment 14 staff members, 3 postdoctoral and 5 doctoral students are involved in doing research within the school.

Main Areas of Research

· Fractal analysis, development of theoretical principles of non-regular structures based on the geometrical theory of functions and theory of continuous and discrete dynamic systems

· Simulation of fractal structures representing continuos and discrete processes of non-equilibrium systems

· Developing a theory of abstract dynamic systems including discrete computer models of the non-difference type.

· Stability of discrete and continuous sets in information flows of dynamic systems

· Computational geometry and modern image theory

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