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Backward orbits of transitive maps
Title Backward orbits of transitive maps Par.title Spätné orbity tranzitívnych zobrazení Author info Peter Maličký Author Maličký Peter 1956- (100%) UMBFP10 - Katedra matematiky
Source document Journal of Difference Equations and Applications. Vol. 18, no. 7 (2012), pp. 1193-1203. - Abingdon : Taylor & Francis Group, 2012 Keywords spätná orbita tranzitívne zobrazenia reziduálna množina analytická množina Bairova vlastnosť backward orbits transitive maps residual set analytic set property of Baire Language English Country Great Britian systematics 517 Annotation 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 Public work category ADC No. of Archival Copy 23321 Repercussion category 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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