Hausdorff-Bezikovich

At present the tendency of polymers mechanics main principles revision is marked. One of the intensively developing trends is coimected with fractal conception using [34], The wide field of this conception in physics different branches is due to two features. The first is connected with using of notions of Hausdorff-Bezikovich fractional dimension geometry. This helped to describe adequately systems with complex spatial structure, what cannot be done within the frameworks of Euclidean geometry. The second feature is connected with fractional integration and differentiation calculus using [35],... 

Self-similar objects, invariant about local dilatations, i.e., objects which in observation processes at various magnifications repeat the same form, are called fractals. Mandelbrot [1] introduced the notion of fractals as self-similar sets, defining a fractal as a set for which the Hausdorff-Bezikovich dimension always exceeds the topological dimension. The fractal dimension d oi the object, adopted in d-dimensional Euclidean space, varies from 1 to d. Fractal objects are natural fillings of sets between known Euclideans with whole number dimensions 0, 1, 2, 3,. .. The majority of objects existing in nature turn out to be fractal ones, which is the main reason for the vigorous development of fractal analysis methods. 

---