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Title Minimal extensions in smooth dynamics Author info Matúš Dirbák Author Dirbák Matúš 1983- (100%) UMBFP10 - Katedra matematiky
Source document Monatshefte für Mathematik. Vol. 4, no. 204 (2024), pp. 783-838. - Viedeň : Springer Nature, 2024 Keywords minimálny tok minimálne rozšírenie Form. Descr. články - journal articles Language English Country Austria Annotation A classical result of Fathi and Herman from 1977 states that a smooth compact connected manifold without boundary admitting a locally free action of a 1-torus, respectively, an almost free action of a 2-torus, admits a minimal diffeomorphism, respectively, a minimal flow. In the first part of our paper we study the existence of locally free and almost free actions of tori on homogeneous spaces of compact connected Lie groups, thus providing new examples of spaces admitting minimal diffeomorphisms or flows. In the second part we combine the ideas of Fathi and Herman with our recent ideas to study the existence of minimal skew products over certain minimal flows with general connected Lie groups as acting groups. Our results apply to so called flows with free cycles. In the last part of our work we study the existence of free cycles in homogeneous flows. URL Link na plný text Public work category ADC No. of Archival Copy 54895 Catal.org. BB301 - Univerzitná knižnica Univerzity Mateja Bela v Banskej Bystrici Database xpca - PUBLIKAČNÁ ČINNOSŤ References PERIODIKÁ-Súborný záznam periodika 
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Title Minimal extensions of flows with amenable acting groups Author info Matúš Dirbák Author Dirbák Matúš 1983- (100%) UMBFP10 - Katedra matematiky
Source document Israel Journal of Mathematics. Vol. 207, no. 2 (2015), pp. 581-615. - Jerusalem : The Hebrew University Magnes Press, 2015 Keywords minimálny tok minimálne rozšírenie amenabelná grupa minimal flow minimal extension amenable group Language English Country Israel systematics 51 Annotation We construct minimal extensions of flows with locally compact amenable acting groups G in the form of fibre-preserving flows on fibre bundles and affine flows on group bundles. We use these constructions to show that for a large family of groups G, the class of the compact second countable spaces, on which G acts in a (point-free and) minimal way, is closed with respect to countable products Public work category ADC No. of Archival Copy 33374 Catal.org. BB301 - Univerzitná knižnica Univerzity Mateja Bela v Banskej Bystrici Database xpca - PUBLIKAČNÁ ČINNOSŤ References PERIODIKÁ-Súborný záznam periodika 
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