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Statements

Subject Item
n2:RIV%2F68407700%3A21110%2F05%3A01117873%21RIV06-GA0-21110___
rdf:type
skos:Concept n16:Vysledek
dcterms:description
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 $\log m$. 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.
dcterms:title
Topoligická entropie m-násobných zobrazení Topological Entropy of m-fold Maps Topological Entropy of m-fold Maps
skos:prefLabel
Topological Entropy of m-fold Maps Topoligická entropie m-násobných zobrazení Topological Entropy of m-fold Maps
skos:notation
RIV/68407700:21110/05:01117873!RIV06-GA0-21110___
n3:strany
375 ; 401
n3:aktivita
n13:P
n3:aktivity
P(GA201/03/1153)
n3:cisloPeriodika
2
n3:dodaniDat
n12:2006
n3:domaciTvurceVysledku
n17:2221306
n3:druhVysledku
n15:J
n3:duvernostUdaju
n18:S
n3:entitaPredkladatele
n9:predkladatel
n3:idSjednocenehoVysledku
546921
n3:idVysledku
RIV/68407700:21110/05:01117873
n3:jazykVysledku
n5:eng
n3:klicovaSlova
level set of a map on compact manifold; topological entropy
n3:klicoveSlovo
n7:topological%20entropy n7:level%20set%20of%20a%20map%20on%20compact%20manifold
n3:kodStatuVydavatele
GB - Spojené království Velké Británie a Severního Irska
n3:kontrolniKodProRIV
[2C3EF4E4001B]
n3:nazevZdroje
Ergodic Theory and Dynamical Systems
n3:obor
n11:BA
n3:pocetDomacichTvurcuVysledku
1
n3:pocetTvurcuVysledku
2
n3:projekt
n10:GA201%2F03%2F1153
n3:rokUplatneniVysledku
n12:2005
n3:svazekPeriodika
25
n3:tvurceVysledku
Nitecki, Z. Bobok, Jozef
s:issn
0143-3857
s:numberOfPages
27
n8:organizacniJednotka
21110