Počet záznamov: 1
Minimal spaces with cyclic group of homeomorphisms
SYS 0244929 LBL ---naa--22--------450- 005 20240513085516.7 014 $a 000395061500012 $2 CCC 014 $a 000395061500012 $2 WOS CC. SCIE 014 $a 2-s2.0-84926204526 $2 SCOPUS 017 70
$a 10.1007/s10884-015-9433-2 $2 DOI 100 $a 20170523 2017 m y slo 03 ba 101 0-
$a eng 102 $a US 200 1-
$a Minimal spaces with cyclic group of homeomorphisms $f Tomasz Downarowicz, Ľubomír Snoha, Dariusz Tywoniuk 330 $a 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. 463 -1
$1 001 umb_un_cat*0293191 $1 011 $a 1040-7294 $1 011 $a 1572-9222 $1 200 1 $a Journal of Dynamics and Differential Equations $v Vol. 29, no. 1 (2017), pp. 243-257 $1 210 $a New York $c Springer $d 2017 606 0-
$3 umb_un_auth*0125697 $a Continuum (Mathematics) 606 0-
$3 umb_un_auth*0207532 $a homeomorphisms 606 0-
$3 umb_un_auth*0039675 $a topologická entropia $X topological entropy 615 $n 51 $a Matematika 675 $a 51 700 -1
$3 umb_un_auth*0160352 $a Downarowicz $b Tomasz $9 34 $4 070 701 -0
$3 umb_un_auth*0022260 $a Snoha $b Ľubomír $p UMBFP10 $4 070 $9 33 $f 1955- $T Katedra matematiky 701 -1
$3 umb_un_auth*0259438 $a Tywoniuk $b Dariusz $4 070 $9 33 801 -0
$a SK $b BB301 $g AACR2 $9 unimarc sk T85 $x existuji fulltexy
Počet záznamov: 1