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JOURNALS // Regular and Chaotic Dynamics // Archive

Regul. Chaotic Dyn., 2010 Volume 15, Issue 2-3, Pages 246–260 (Mi rcd492)

On the 75th birthday of Professor L.P. Shilnikov

Noninvertible maps and their embedding into higher dimensional invertible maps

C. Mira

19 rue d’Occitanie Fonsegrives, 31130 Quint, France

Abstract: The first part is devoted to a presentation of specific features of noninvertible maps with respect to the invertible ones. When embedded into a three-dimensional invertible map, the specific dynamical features of a plane noninvertible map are the germ of the three-dimensional dynamics, at least for sufficiently small absolute values of the embedding parameter. The form of the paper, as well as its contents, is approached from a non abstract point of view, in an elementary form from a simple class of examples.

Keywords: noninvertible maps, embedding problems, discrete dynamics, global bifurcations, critical sets, basin of attraction, fractal sets.

MSC: 10.1134/S1560354710020127

Received: 15.11.2009
Accepted: 23.12.2010

Language: English

DOI: 10.1134/S1560354710020127



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