Introduction to Completely Geometrically Integrable Maps in High Dimensions

Lyudmila S. Efremova ()
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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

Mathematics, 2023, vol. 11, issue 4, 1-14

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.

Keywords: (completely) geometrically integrable map; quotient; local lamination; skew product; periodic point (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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