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

For citation:

Kuznetsov A. P., Sedova Y. V. Bifurcations of three­ and four­dimensional maps: universal properties. Izvestiya VUZ. Applied Nonlinear Dynamics, 2012, vol. 20, iss. 5, pp. 26-43. DOI: 10.18500/0869-6632-2012-20-5-26-43

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Language: 
Russian
Heading: 
Methodical Papers on Nonlinear Dynamics
Article type: 
Article
UDC: 
517.9
DOI: 
10.18500/0869-6632-2012-20-5-26-43

Bifurcations of three­ and four­dimensional maps: universal properties

Autors: 
Kuznetsov Aleksandr Petrovich, Saratov Branch of Kotel`nikov Institute of Radiophysics and Electronics of Russian Academy of Sciences
Sedova Yuliya Viktorovna, Saratov Branch of Kotel`nikov Institute of Radiophysics and Electronics of Russian Academy of Sciences
Abstract: 

The approach, in which the picture of bifurcations of discrete maps is considered in the space of invariants of perturbation matrix (Jacobi matrix), is extended to the case of three and four dimensions. In those cases the structure of surfaces, lines and points for bifurcations, that is universal for all maps, is revealed. We present the examples of maps, whose parameters are governed directly by invariants of the Jacobian matrix.

Key words: 
maps
bifurcations
multiplier
perturbation matrix
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Received: 
15.02.2012
Accepted: 
15.02.2012
Published: 
31.01.2013
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