In the previous papers, the author offered a new theory of topological invariants for the dynamical systems formed by noninvertible inner mappings. These invariants are constructed by using the analogy between the trajectories of homeomorphisms and directions in the set of points with common iteration. In particular, we introduce the sets of neutrally recurrent and neutrally nonwandering points. We also present an example of the so-called “neutrally nonwandering but not neutrally recurrent” points, which shows that these sets do not coincide.
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I. Yu. Vlasenko, “Dynamics of inner mappings,” Nelin. Kolyv., 14, No. 2, 181–186 (2011); English translation: Nonlin. Oscillat., 14, No. 2, 187–192 (2011).
I. Yu. Vlasenko, Inner Mappings: Topological Invariants and Their Applications, Proc. of the Institute of Mathematics, Ukrainian National Academy of Sciences, Kyiv (2014).
V. Z. Grines and O. V. Pochinka, Introduction to the Topological Classification of Cascades on Manifolds of Dimensions Two and Three [in Russian], Regulyar. Khaotich. Dinam., Moscow–Izhevsk (2011).
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 67, No. 8, pp. 1030–1033, August, 2015.
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Vlasenko, I.Y. An Example of Neutrally Nonwandering Points for the Inner Mappings that are Not Neutrally Recurrent. Ukr Math J 67, 1159–1163 (2016). https://doi.org/10.1007/s11253-016-1143-3
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DOI: https://doi.org/10.1007/s11253-016-1143-3