About: On variants of distributional chaos in dimension one

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Attributes	Values
rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
rdfs:seeAlso	http://www.tandfonline.com/doi/abs/10.1080/14689367.2011.588199
Description	In their famous paper from 1994, B. Schwaizer and J. Smital, [B. Schwaizer and J. Smital, Measures of chaos and a spectral decomposition of dynamical systems on the interval, Trans. Amer. Math. Soc. 344 (1994), pp. 737-754] fully characterized topological entropy of interval maps in terms of distribution functions of distance between trajectories. Strictly speaking, they proved that a continuous map f :[0, 1]->[0, 1] has zero topological entropy if and only if for every x, y is an element of [0, 1] the following limit exists: lim(n -> infinity) 1/n vertical bar{0 <= i < n : d (f(i)(x),f(i)(y)) < t}vertical bar for every real number t except at most countable set. While many partial efforts have been made in previous years, still there is no proof that the result of Schwaizer and Smital holds on every topological graph. Here we offer the proof of this fact, filling a gap existing in the literature of the topic. In their famous paper from 1994, B. Schwaizer and J. Smital, [B. Schwaizer and J. Smital, Measures of chaos and a spectral decomposition of dynamical systems on the interval, Trans. Amer. Math. Soc. 344 (1994), pp. 737-754] fully characterized topological entropy of interval maps in terms of distribution functions of distance between trajectories. Strictly speaking, they proved that a continuous map f :[0, 1]->[0, 1] has zero topological entropy if and only if for every x, y is an element of [0, 1] the following limit exists: lim(n -> infinity) 1/n vertical bar{0 <= i < n : d (f(i)(x),f(i)(y)) < t}vertical bar for every real number t except at most countable set. While many partial efforts have been made in previous years, still there is no proof that the result of Schwaizer and Smital holds on every topological graph. Here we offer the proof of this fact, filling a gap existing in the literature of the topic. (en)
Title	On variants of distributional chaos in dimension one On variants of distributional chaos in dimension one (en)
skos:prefLabel	On variants of distributional chaos in dimension one On variants of distributional chaos in dimension one (en)
skos:notation	RIV/47813059:19610/11:#0000301!RIV12-MSM-19610___
http://linked.open...avai/predkladatel	Matematický ústav v Opavě
http://linked.open...avai/riv/aktivita	Z
http://linked.open...avai/riv/aktivity	Z(MSM4781305904)
http://linked.open...iv/cisloPeriodika	3
http://linked.open...vai/riv/dodaniDat	2012
http://linked.open...aciTvurceVysledku	Málek, Michal
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	Slezská univerzita v Opavě / Matematický ústav v Opavě
http://linked.open...dnocenehoVysledku	218328
http://linked.open...ai/riv/idVysledku	RIV/47813059:19610/11:#0000301
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	distributional chaos; scrambled set; topological entropy; topological graph (en)
http://linked.open.../riv/klicoveSlovo	topological graph distributional chaos scrambled set topological entropy
http://linked.open...odStatuVydavatele	GB - Spojené království Velké Británie a Severního Irska
http://linked.open...ontrolniKodProRIV	[618611D84586]
http://linked.open...i/riv/nazevZdroje	Dynamical Systems: An International Journal
http://linked.open...in/vavai/riv/obor	BA
http://linked.open...ichTvurcuVysledku	1 (xsd:int)
http://linked.open...cetTvurcuVysledku	2 (xsd:int)
http://linked.open...UplatneniVysledku	2011
http://linked.open...v/svazekPeriodika	26
http://linked.open...iv/tvurceVysledku	Málek, Michal Oprocha, Piotr
http://linked.open...ain/vavai/riv/wos	000299632100004
http://linked.open...n/vavai/riv/zamer	Topological and analytical methods in the theory of dynamical systems and mathematical physics
issn	1468-9367
number of pages	13 (xsd:int)
http://bibframe.org/vocab/doi	10.1080/14689367.2011.588199
http://localhost/t...ganizacniJednotka	19610
is http://linked.open...avai/riv/vysledek of	On variants of distributional chaos in dimension one On variants of distributional chaos in dimension one

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