About: The Topological Entropy versus Level Sets for Interval Maps (part II)

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
Description	Let $f\colon~ [a,b]\to [a,b]$ be a continuous function of the compact real interval such that (i) $\card f^{-1}(y)\ge 2$ for every point $y\in [a,b]$; (ii) for some $m\in\{\infty,2,3,\dots\}$ there is a countable set $L\subset [a,b]$ such that $\card f^{-1}(y)\ge m$ for every point $y\in [a,b]\setminus L$ . We show that the topological entropy of $f$ is greater than or equal to $\log m$. This result generalizes our previous one stated for $m=2$. Let $f\colon~ [a,b]\to [a,b]$ be a continuous function of the compact real interval such that (i) $\card f^{-1}(y)\ge 2$ for every point $y\in [a,b]$; (ii) for some $m\in\{\infty,2,3,\dots\}$ there is a countable set $L\subset [a,b]$ such that $\card f^{-1}(y)\ge m$ for every point $y\in [a,b]\setminus L$ . We show that the topological entropy of $f$ is greater than or equal to $\log m$. This result generalizes our previous one stated for $m=2$. (en) Článek navazuje na autorův důkaz Covenovy hypotézy, že entropie intervalového zobrazení, jehož každá úrovňová množina má alespoň dva prvky, není menší než log2. (cs)
Title	The Topological Entropy versus Level Sets for Interval Maps (part II) Topologická entropie a úrovňové množiny pro intervalová zobrazení (část II) (cs) The Topological Entropy versus Level Sets for Interval Maps (part II) (en)
skos:prefLabel	The Topological Entropy versus Level Sets for Interval Maps (part II) Topologická entropie a úrovňové množiny pro intervalová zobrazení (část II) (cs) The Topological Entropy versus Level Sets for Interval Maps (part II) (en)
skos:notation	RIV/68407700:21110/05:01117871!RIV06-GA0-21110___
http://linked.open.../vavai/riv/strany	11 ; 27
http://linked.open...avai/riv/aktivita	P
http://linked.open...avai/riv/aktivity	P(GA201/00/0859)
http://linked.open...iv/cisloPeriodika	1
http://linked.open...vai/riv/dodaniDat	2006
http://linked.open...aciTvurceVysledku	Bobok, Jozef
http://linked.open.../riv/druhVysledku	J - Článek v odborném periodiku
http://linked.open...iv/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open...titaPredkladatele	České vysoké učení technické v Praze / Fakulta stavební
http://linked.open...dnocenehoVysledku	546922
http://linked.open...ai/riv/idVysledku	RIV/68407700:21110/05:01117871
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	level set of interval map; topological entropy (en)
http://linked.open.../riv/klicoveSlovo	topological entropy level set of interval map
http://linked.open...odStatuVydavatele	PL - Polská republika
http://linked.open...ontrolniKodProRIV	[EA814D899B62]
http://linked.open...i/riv/nazevZdroje	Studia Mathematica
http://linked.open...in/vavai/riv/obor	BA
http://linked.open...ichTvurcuVysledku	1 (xsd:int)
http://linked.open...cetTvurcuVysledku	1 (xsd:int)
http://linked.open...vavai/riv/projekt	Dynamical systems
http://linked.open...UplatneniVysledku	2005
http://linked.open...v/svazekPeriodika	166
http://linked.open...iv/tvurceVysledku	Bobok, Jozef
issn	0039-3223
number of pages	17 (xsd:int)
http://localhost/t...ganizacniJednotka	21110

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