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  • We investigate the relation between preimage multiplicity and topological entropy for continuous maps. An argument originated by Misiurewicz and Przytycki shows that if every regular value of a $C^{1}$ map has at least $m$ preimages then the topological entropy of the map is at least $\log m$. For every integer, there exist continuous maps of the circle with entropy zero for which every point has at least $m$ preimages. We show that if in addition there is a positive uniform lower bound on the diameter of all pointwise preimage sets, then the entropy is at least $\log m$.
  • We investigate the relation between preimage multiplicity and topological entropy for continuous maps. An argument originated by Misiurewicz and Przytycki shows that if every regular value of a $C^{1}$ map has at least $m$ preimages then the topological entropy of the map is at least $\log m$. For every integer, there exist continuous maps of the circle with entropy zero for which every point has at least $m$ preimages. We show that if in addition there is a positive uniform lower bound on the diameter of all pointwise preimage sets, then the entropy is at least $\log m$. (en)
  • V článku je vyšetřována závislost topologické entropie a počtu prvků úrovňových množin C^1-zobrazení kompaktní variety do sebe. Pro kružnici jsou dokázány výsledky bez předpokladu hladkosti. (cs)
Title
  • Topological Entropy of m-fold Maps
  • Topoligická entropie m-násobných zobrazení (cs)
  • Topological Entropy of m-fold Maps (en)
skos:prefLabel
  • Topological Entropy of m-fold Maps
  • Topoligická entropie m-násobných zobrazení (cs)
  • Topological Entropy of m-fold Maps (en)
skos:notation
  • RIV/68407700:21110/05:01117873!RIV06-GA0-21110___
http://linked.open.../vavai/riv/strany
  • 375 ; 401
http://linked.open...avai/riv/aktivita
http://linked.open...avai/riv/aktivity
  • P(GA201/03/1153)
http://linked.open...iv/cisloPeriodika
  • 2
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
  • 546921
http://linked.open...ai/riv/idVysledku
  • RIV/68407700:21110/05:01117873
http://linked.open...riv/jazykVysledku
http://linked.open.../riv/klicovaSlova
  • level set of a map on compact manifold; topological entropy (en)
http://linked.open.../riv/klicoveSlovo
http://linked.open...odStatuVydavatele
  • GB - Spojené království Velké Británie a Severního Irska
http://linked.open...ontrolniKodProRIV
  • [2C3EF4E4001B]
http://linked.open...i/riv/nazevZdroje
  • Ergodic Theory and Dynamical Systems
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
  • 25
http://linked.open...iv/tvurceVysledku
  • Bobok, Jozef
  • Nitecki, Z.
issn
  • 0143-3857
number of pages
http://localhost/t...ganizacniJednotka
  • 21110
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