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  • It is well known that for dynamical systems generated by continuous maps of a graph, the centre of the dynamical system is a subset of the set of omega-limit points. In this paper we provide an example of a continuous self-map f(1) of a dendrite such that omega(f(1)) is a proper subset of C(f(1)). The second example is a continuous self-map f(2) of a dendrite having a strictly increasing sequence of omega-limit sets which is not contained in any maximal one. Again, this is impossible for continuous maps on graphs.
  • It is well known that for dynamical systems generated by continuous maps of a graph, the centre of the dynamical system is a subset of the set of omega-limit points. In this paper we provide an example of a continuous self-map f(1) of a dendrite such that omega(f(1)) is a proper subset of C(f(1)). The second example is a continuous self-map f(2) of a dendrite having a strictly increasing sequence of omega-limit sets which is not contained in any maximal one. Again, this is impossible for continuous maps on graphs. (en)
Title
  • On the centre and the set of omega-limit points of continuous maps on dendrites
  • On the centre and the set of omega-limit points of continuous maps on dendrites (en)
skos:prefLabel
  • On the centre and the set of omega-limit points of continuous maps on dendrites
  • On the centre and the set of omega-limit points of continuous maps on dendrites (en)
skos:notation
  • RIV/47813059:19610/09:#0000258!RIV10-GA0-19610___
http://linked.open...avai/riv/aktivita
http://linked.open...avai/riv/aktivity
  • P(GA201/06/0318), Z(MSM4781305904)
http://linked.open...iv/cisloPeriodika
  • 18
http://linked.open...vai/riv/dodaniDat
http://linked.open...aciTvurceVysledku
http://linked.open.../riv/druhVysledku
http://linked.open...iv/duvernostUdaju
http://linked.open...titaPredkladatele
http://linked.open...dnocenehoVysledku
  • 331486
http://linked.open...ai/riv/idVysledku
  • RIV/47813059:19610/09:#0000258
http://linked.open...riv/jazykVysledku
http://linked.open.../riv/klicovaSlova
  • omega-limit set; Recurrent point; Centre of dynamical system; Dendrite (en)
http://linked.open.../riv/klicoveSlovo
http://linked.open...odStatuVydavatele
  • NL - Nizozemsko
http://linked.open...ontrolniKodProRIV
  • [CDD4B9AD1878]
http://linked.open...i/riv/nazevZdroje
  • Topology and its Applications
http://linked.open...in/vavai/riv/obor
http://linked.open...ichTvurcuVysledku
http://linked.open...cetTvurcuVysledku
http://linked.open...vavai/riv/projekt
http://linked.open...UplatneniVysledku
http://linked.open...v/svazekPeriodika
  • 156
http://linked.open...iv/tvurceVysledku
  • Kornecká-Kurková, Veronika
  • Kočan, Zdeněk
  • Málek, Michal
http://linked.open...ain/vavai/riv/wos
  • 000271159900004
http://linked.open...n/vavai/riv/zamer
issn
  • 0166-8641
number of pages
http://localhost/t...ganizacniJednotka
  • 19610
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