Open AccessConstruction of Energetic Functions for Ω-Stable Diffeomorphisms on 2and 3-Manifolds
Author(s) -
Vyacheslav Zigmuntovich Grines,
O. V. Pochinka
Publication year - 2017
Publication title -
sovremennaâ matematika. fundamentalʹnye napravleniâ
Language(s) - English
Resource type - Journals
eISSN - 2949-0618
pISSN - 2413-3639
DOI - 10.22363/2413-3639-2017-63-2-191-222
Subject(s) - dimension (graph theory) , pure mathematics , function (biology) , mathematics , manifold (fluid mechanics) , dynamical systems theory , stability (learning theory) , physics , computer science , engineering , biology , evolutionary biology , mechanical engineering , quantum mechanics , machine learning
In this paper, we review the results connected to existence of the energetic function for discrete dynamical systems. Also we consider technique of construction of such functions for some classes of Ωstable and structurally stable dieomorphisms on manifolds of dimension 2 and 3.