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Proper minimal sets on compact connected 2-manifolds are nowhere dense
Názov Proper minimal sets on compact connected 2-manifolds are nowhere dense Súbež.n. Vlastné minimálne množiny na kompaktných súvislých 2-varietách sú riedke Aut.údaje Sergii Kolyada, Ľubomír Snoha, Sergei Trofimchuk Autor Kolyada Sergiy (34%)
Spoluautori Snoha Ľubomír 1955- (33%) UMBFP10 - Katedra matematiky
Trofimchuk Sergei (33%)
Zdroj.dok. Ergodic Theory and Dynamical Systems. Vol. 28, no. 3 (2008), pp. 863-876. - Cambridge : Cambridge University Press, 2008 Kľúč.slová variety (matematika) - manifolds (mathematics) minimálne množiny kaktoidy manifolds minimal sets cactoids Jazyk dok. angličtina Krajina Veľká Británia Systematika 51 Anotácia Let $/mathcal{M}^2$ be a compact connected 2-dimensional manifold, with or without boundary, and let $f:{/mathcal{M}}^2/to /mathcal{M}^2$ be a continuous map. We prove that if $M /subseteq /mathcal{M}^2$ is a minimal set of the dynamical system $(/mathcal{M}^2,f)$ then either $M = /mathcal{M}^2$ or $M$ is a nowhere dense subset of $/mathcal{M}^2$. Moreover, we add a shorter proof of the recent result of Blokh, Oversteegen and Tymchatyn, that in the former case $/mathcal{M}^2$ is a torus or a Klein bottle Kategória publikačnej činnosti ADC Číslo archívnej kópie 9927 Kategória ohlasu VLASENKO, I. Yu. Dynamics of inner mappings. In Nonlinear oscillations. ISSN 1536-0059, 2011, vol. 14, no. 2, pp. 187-192.
MAI, Jie-Hua. Minimal sets in compact connected subspaces. In Topology and its applications. ISSN 0166-8641, 2011, vol. 158, no. 16, pp. 2216-2220.
DIRBAK, Matus. Minimal extensions of flows with amenable acting groups. In Israel journal of mathematics. ISSN 0021-2172, 2015, vol. 207, no. 2, pp. 581-615.
BIS, Andrzej - KOZLOWSKI, Wojciech. On minimal homeomorphisms and non-invertible maps preserving foliations. In Topology and its applications. ISSN 0166-8641, 2019, vol. 254, DOI 10.1016/j.topol.2018.11.024, pp. 1-11.
PARHAM, H. - GHANE, F. H. - EHSANI, A. Iterated function systems : transitivity and minimality. In Boletim da Sociedade Paranaense de Matemática. ISSN 0037-8712, 2020, vol. 38, no. 3, pp. 97-109.
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