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Minimal spaces with cyclic group of homeomorphisms
Názov Minimal spaces with cyclic group of homeomorphisms Aut.údaje Tomasz Downarowicz, Ľubomír Snoha, Dariusz Tywoniuk Autor Downarowicz Tomasz (34%)
Spoluautori Snoha Ľubomír 1955- (33%) UMBFP10 - Katedra matematiky
Tywoniuk Dariusz (33%)
Zdroj.dok. Journal of Dynamics and Differential Equations. Vol. 29, no. 1 (2017), pp. 243-257. - New York : Springer, 2017 Kľúč.slová Continuum (Mathematics) homeomorphisms topologická entropia - topological entropy Jazyk dok. angličtina Krajina Spojené štáty Systematika 51 Anotácia There are two main subjects in this paper. (1) For a topological dynamical system we study the topological entropy of its "functional envelopes" (the action of by left composition on the space of all continuous self-maps or on the space of all self-homeomorphisms of ). In particular we prove that for zero-dimensional spaces both entropies are infinite except when is equicontinuous (then both equal zero). (2) We call Slovak space any compact metric space whose homeomorphism group is cyclic and generated by a minimal homeomorphism. Using Slovak spaces we provide examples of (minimal) systems with positive entropy, yet, whose functional envelope on homeomorphisms has entropy zero (answering a question posed by Kolyada and Semikina). Finally, also using Slovak spaces, we resolve a long standing open problem whether the circle is a unique non-degenerate continuum admitting minimal continuous transformations but only invertible: No, some Slovak spaces are such, as well. Kategória publikačnej činnosti ADC Číslo archívnej kópie 39386 Kategória ohlasu AKIN, Ethan - RAUTIO, Juho. Chain transitive homeomorphisms on a space: all or none. In Pacific journal of mathematics. ISSN 0030-8730, 2017, vol. 291, no. 1, pp. 1-49.
BORONSKI, J. P. - CLARK, Alex - OPROCHA, P. A compact minimal space Y such that its square Y x Y is not minimal. In Advances in mathematics. ISSN 0001-8708, 2018, vol. 335, pp. 261-275.
KOLYADA, Sergii. A survey of some aspects of dynamical topology : dynamical compactness and Slovak spaces. In Discrete and continuous dynamical systems : series S. ISSN 1937-1632, 2020, vol. 13, no. 4, pp. 1291-1317.
BORONSKI, Jan P. - CINC, Jernej - FORYS-KRAWIEC, Magdalena. On rigid minimal spaces. In Journal of dynamics and differential equations. ISSN 1040-7294, 2021, vol. 33, no. 2, pp. 1023-1034.
BORONSKI, Jan P. - KENNEDY, Judy - LIU, Xiao-Chuan - OPROCHA, Piotr. Minimal non-invertible maps on the pseudo-circle. In Journal of dynamics and differential equations. ISSN 1040-7294, 2021, vol. 33, no. 4, pp. 1897-1916.
BORONSKI, Jan P. - CLARK, Alex - OPROCHA, Piotr. New exotic minimal sets from pseudo-suspensions of cantor systems. In Journal of dynamics and differential equations. ISSN 1040-7294, 2021, vol. 35, no. 2, pp. 1175-1201.
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