Anotácia | Pre diskrétny dynamický priestor určený poským priestorom X a spojitým zobrazením f priestoru X do seba skúmame množinu D tých bodov, ktoré majú nejakú hustú spätnú orbitu. Dokazujeme, že pre tranzitívne zobrazenie f je množina D analytická, ktorá má mohutnusť kontinua dokonca lokálne. Za predpokladu, ze f je navyše skoro slabo otvorené je množina D reziduálna. For a discrete dynamical system given by a Polish space X and a continuous selfmap f of X we investigate the set D of all points which have some dense backward orbit. It is proved that if f is a topologically transitive map then D is an analytic set which has the continuum power even locally. Under the additional assumption that f is nearly feebly open, the set D is residual
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Kategória ohlasu | MOOTHATHU, T. K. Subrahmonian. The speed with which an orbit approaches a limit point. In Journal of difference equations and applications. ISSN 1023-6198, 2012, vol. 18, no. 10, pp. 1611-1621. DIRBAK, Matus - SNOHA, Lubomir - SPITALSKY, Vladimir. Minimality, transitivity, mixing and topological entropy on spaces with a free interval. In Ergodic theory and dynamical systems. ISSN 0143-3857, 2013, vol. 33, pp. 1786-1812. BLANCHARD, François - HUANG, Wen - SNOHA, Ľubomír. Topological size of scrambled sets. In Colloquium mathematicum. ISSN 0010-1354, 2008, vol. 110, no. 2, pp. 293-361. KOLYADA, S. - SNOHA, L. - TROFIMCHUK, S. Noninvertible minimal maps. In Fundamenta mathematicae. ISSN 0016-2736, 2001, vol. 168, no. 2, pp. 141-163. KOLYADA, Sergii - SNOHA, Lubomir - TROFIMCHUK, Sergei. Minimal sets of fibre-preserving maps in graph bundles. In Mathemathische Zeitschrift. ISSN 0025-5874, 2014, vol. 278, no. 1-2, pp. 575-614. TAKACS, Michal. Generic chaos on graphs. In Journal of difference equations and applications. ISSN 1023-6198, 2016, vol. 22, no. 1, pp. 1-21.
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