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rdf:type
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Description
| - We show that there is a continuous map $\chi$ of the unit interval into itself of type $2^\infty$ which has a trajectory disjoint from the set $ \operatorname{Rec}(\chi )$ of recurrent points of $\chi$, but contained in the closure of $ \operatorname{Rec}(\chi )$. In particular, $ \operatorname{Rec}(\chi )$ is not closed. A function $\psi$ of type $2^\infty$, with nonclosed set of recurrent points, was found by H. Chu and J. Xiong [Proc. Amer. Math. Soc. 97 (1986), 361-366]. However, there is no trajectory contained in $\overline {\operatorname{Rec} (\psi)}\setminus \operatorname{Rec}(\psi)$, since any point in $\overline { \operatorname{Rec}(\psi)}$ is eventually mapped into $\operatorname{Rec} (\psi)$. Moreover, our construction is simpler. We use $\chi$ to show that there is a continuous map of the interval of type $2^\infty$ for which the set of recurrent points is not an $F_\sigma$ set. This example disproves a conjecture of A. N. Sharkovsky-1989
- We show that there is a continuous map $\chi$ of the unit interval into itself of type $2^\infty$ which has a trajectory disjoint from the set $ \operatorname{Rec}(\chi )$ of recurrent points of $\chi$, but contained in the closure of $ \operatorname{Rec}(\chi )$. In particular, $ \operatorname{Rec}(\chi )$ is not closed. A function $\psi$ of type $2^\infty$, with nonclosed set of recurrent points, was found by H. Chu and J. Xiong [Proc. Amer. Math. Soc. 97 (1986), 361-366]. However, there is no trajectory contained in $\overline {\operatorname{Rec} (\psi)}\setminus \operatorname{Rec}(\psi)$, since any point in $\overline { \operatorname{Rec}(\psi)}$ is eventually mapped into $\operatorname{Rec} (\psi)$. Moreover, our construction is simpler. We use $\chi$ to show that there is a continuous map of the interval of type $2^\infty$ for which the set of recurrent points is not an $F_\sigma$ set. This example disproves a conjecture of A. N. Sharkovsky-1989 (en)
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Title
| - A zero topological entropy map with recurrent points not $F\sb \sigma$
- A zero topological entropy map with recurrent points not $F\sb \sigma$ (en)
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skos:prefLabel
| - A zero topological entropy map with recurrent points not $F\sb \sigma$
- A zero topological entropy map with recurrent points not $F\sb \sigma$ (en)
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skos:notation
| - RIV/47813059:19610/03:00000121!RIV/2004/MSM/196104/N
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http://linked.open.../vavai/riv/strany
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http://linked.open...avai/riv/aktivita
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http://linked.open...avai/riv/aktivity
| - P(GA201/00/0859), Z(MSM 192400002)
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http://linked.open...iv/cisloPeriodika
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http://linked.open...vai/riv/dodaniDat
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http://linked.open...aciTvurceVysledku
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http://linked.open.../riv/druhVysledku
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http://linked.open...iv/duvernostUdaju
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http://linked.open...titaPredkladatele
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http://linked.open...dnocenehoVysledku
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http://linked.open...ai/riv/idVysledku
| - RIV/47813059:19610/03:00000121
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http://linked.open...riv/jazykVysledku
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http://linked.open.../riv/klicovaSlova
| - Topological entropy; recurrent points; periodic points; $\omega$-limit s (en)
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http://linked.open.../riv/klicoveSlovo
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http://linked.open...odStatuVydavatele
| - US - Spojené státy americké
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http://linked.open...ontrolniKodProRIV
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http://linked.open...i/riv/nazevZdroje
| - Proceedings of the American Mathematical Society
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http://linked.open...in/vavai/riv/obor
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http://linked.open...ichTvurcuVysledku
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http://linked.open...cetTvurcuVysledku
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http://linked.open...ocetUcastnikuAkce
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http://linked.open...nichUcastnikuAkce
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http://linked.open...vavai/riv/projekt
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http://linked.open...UplatneniVysledku
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http://linked.open...v/svazekPeriodika
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http://linked.open...iv/tvurceVysledku
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http://linked.open...n/vavai/riv/zamer
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issn
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number of pages
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http://localhost/t...ganizacniJednotka
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