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

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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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Bifurcations of three­ and four­dimensional maps: universal properties

Kuznetsov Aleksandr Petrovich, Saratov Branch of Kotel`nikov Institute of Radiophysics and Electronics of Russian Academy of Sciences
Sedova Yu. V., Saratov Branch of Kotel`nikov Institute of Radiophysics and Electronics of Russian Academy of Sciences

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.

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