Abstract
In this paper, we review results related to the existence of the energy function for discrete dynamical systems. Also, we consider the technique of constructing such functions for various classes of Ω-stable and structurally stable diffeomorphisms on manifolds of dimension 2 and 3.
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Translated from Sovremennaya Matematika. Fundamental’nye Napravleniya (Contemporary Mathematics. Fundamental Directions), Vol. 63, No. 2, Proceedings of the Crimean Autumn Mathematical School-Symposium, 2017.
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Grines, V.Z., Pochinka, O.V. The Constructing of Energy Functions for Ω-Stable Diffeomorphisms on 2- and 3-Manifolds. J Math Sci 250, 537–568 (2020). https://doi.org/10.1007/s10958-020-05028-0
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DOI: https://doi.org/10.1007/s10958-020-05028-0