For citation:
Tlyachev V. B., Ushkho A. D., Ushkho D. S. Symmetry Axes of Planar Polynomial Differential Systems. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2010, vol. 10, iss. 2, pp. 41-49. DOI: 10.18500/1816-9791-2010-10-2-41-49
This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Published online:
18.01.2010
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Language:
Russian
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UDC:
517.917
Symmetry Axes of Planar Polynomial Differential Systems
Autors:
Tlyachev V. B., Caucasus Mathematical Center Adyghe State University
Ushkho A. D., Caucasus Mathematical Center Adyghe State University
Ushkho D. S., Caucasus Mathematical Center Adyghe State University
Abstract:
The notion of N-type axis of symmetry is introduced. It is proved that the vector field defined by system of the differential equations with norder polynomials in a right hand, cannot have even number of axes of symmetry N-type at n =2m,m ∈N. For n =2,3 full research of the given system on N-symmetry is carried out. Depending on the number of axes of N-type symmetry special forms of presenting of square and cubic systems, which allow to simplify qualitative research of such systems, are discovered.
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