Geodesic
A brief review of the research results of new methods for generating, transmitting and receiving oscillations and waves based on fractal geometry methods
Izvestiya VUZ. Applied Nonlinear Dynamics, Tome 28 (2020) no. 1, pp. 8-28.

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Purpose of this article is to generalize results of the application of fractal geometry methods in various radiophysic systems and at study of processes occurring in them. Methods. The presentation is built in the form of a brief review of a number of works devoted to new methods for generating, receiving and transmitting signals of various frequency ranges, including microwave frequencies, using fractal geometry approaches. At the same time, it was advisable to give examples of constructing such classical fractals as the Peano curve, Sierpinski triangle and Sierpinski carpet, Koch curve, etc., and indicate the Hausdorff dimension for them. The idea of constructing these fractal curves and objects with some modifications underlies the creation of real physical systems. Results.The review showed that fractal objects are actively used in the design of fractal antennas, fractal resonators and filters built on their basis. Taking into account the fractal surface of the cathode also gives certain advantages and explains some experimental results. Some other fields of application of fractals are indicated, where the complexity of spatial or temporal structures at different scales plays an important role. It should be noted that the artificially created elements in question are self-similar only to a certain extent, representing the first few iterations of constructing fractal curves. In this regard, they are called as quasi-fractal or prefractal objects. Conclusion. Formation of fractal thinking and the fractal view of the world as a whole made it possible to use the principles of self-similarity in the analysis of work and the design of devices. The obvious advantages were a possible reduction in size, the expansion of the frequency range of the device, etc.
Keywords: fractal, Hausdorff-Besicovitch dimension, fractal antennas, fractal resonators, fractal cathodes. 
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     author = {G. M. Vdovina},
     title = {A brief review of the research results of new methods for generating, transmitting and receiving oscillations and waves based on fractal geometry methods},
     journal = {Izvestiya VUZ. Applied Nonlinear Dynamics},
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G. M. Vdovina. A brief review of the research results of new methods for generating, transmitting and receiving oscillations and waves based on fractal geometry methods. Izvestiya VUZ. Applied Nonlinear Dynamics, Tome 28 (2020) no. 1, pp. 8-28. http://geodesic.mathdoc.fr/item/IVP_2020_28_1_a1/