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Introduction to Completely Geometrically Integrable Maps in High Dimensions

Author

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  • Lyudmila S. Efremova

    (Institute of Information Technologies, Mathematics and Mechanics, Nizhny Novgorod State University, Gagarin Ave, Nizhny Novgorod 603022, Nizhny Novgorod, Russia
    Department of General Mathematics, Moscow Institute of Physics and Technologies, Institutskii per, Dolgoprudny 141701, Moscow Region, Russia)

Abstract

We introduce here the concept of completely geometrically integrable self-maps of n -dimensional ( n ≥ 2 ) cells, cylinders and tori. This concept is the extension of the geometric integrability concept previously introduced for the self-maps of a rectangle in the plane. We formulate and prove here the criteria for the complete geometric integrability of maps on the cells, cylinders and tori of high dimensions. As a corollary of these results, we obtain, in particular, the generalization of the famous Sharkovsky’s Theorem for the set of periods of periodic points of completely geometrically integrable self-maps of multidimensional cells.

Suggested Citation

  • Lyudmila S. Efremova, 2023. "Introduction to Completely Geometrically Integrable Maps in High Dimensions," Mathematics, MDPI, vol. 11(4), pages 1-14, February.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:4:p:926-:d:1065943
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