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Statements

Subject Item
n2:RIV%2F68407700%3A21110%2F11%3A00189602%21RIV12-MSM-21110___
rdf:type
n6:Vysledek skos:Concept
dcterms:description
We investigate continuous piecewise affine interval maps with count-ably many laps that preserve the Lebesgue measure. In particular, we construct such maps having knot points (a point x where Dini's derivatives satisfy D^+f(x) = D^-f(x) = infinity and D_+f(x) = D_-f(x) = - infinity) and estimate their topological entropy. Our main result is: for any epsilon > 0 we construct a continuous interval map g = g_epsilon such that (i) g preserves the Lebesgue measure; (ii) knot points of g are dense in [0; 1] and for a G_delta dense set of z's, the set g^-1({z}) is infinite; (iii) h_top(g)<= log2+epsilon. We investigate continuous piecewise affine interval maps with count-ably many laps that preserve the Lebesgue measure. In particular, we construct such maps having knot points (a point x where Dini's derivatives satisfy D^+f(x) = D^-f(x) = infinity and D_+f(x) = D_-f(x) = - infinity) and estimate their topological entropy. Our main result is: for any epsilon > 0 we construct a continuous interval map g = g_epsilon such that (i) g preserves the Lebesgue measure; (ii) knot points of g are dense in [0; 1] and for a G_delta dense set of z's, the set g^-1({z}) is infinite; (iii) h_top(g)<= log2+epsilon.
dcterms:title
Irreducibility, Infinite Level Sets,and Small Entropy Irreducibility, Infinite Level Sets,and Small Entropy
skos:prefLabel
Irreducibility, Infinite Level Sets,and Small Entropy Irreducibility, Infinite Level Sets,and Small Entropy
skos:notation
RIV/68407700:21110/11:00189602!RIV12-MSM-21110___
n6:predkladatel
n15:orjk%3A21110
n3:aktivita
n8:P n8:Z
n3:aktivity
P(GA201/09/0854), Z(MSM6840770010)
n3:cisloPeriodika
2
n3:dodaniDat
n10:2012
n3:domaciTvurceVysledku
n14:2221306 n14:6836291
n3:druhVysledku
n4:J
n3:duvernostUdaju
n11:S
n3:entitaPredkladatele
n18:predkladatel
n3:idSjednocenehoVysledku
205852
n3:idVysledku
RIV/68407700:21110/11:00189602
n3:jazykVysledku
n16:eng
n3:klicovaSlova
interval map, knot point, Lebesgue measure, topological entropy
n3:klicoveSlovo
n7:Lebesgue%20measure n7:interval%20map n7:topological%20entropy n7:knot%20point
n3:kodStatuVydavatele
US - Spojené státy americké
n3:kontrolniKodProRIV
[1596DC5D1AF5]
n3:nazevZdroje
Real Analysis Exchange
n3:obor
n12:BA
n3:pocetDomacichTvurcuVysledku
2
n3:pocetTvurcuVysledku
2
n3:projekt
n19:GA201%2F09%2F0854
n3:rokUplatneniVysledku
n10:2011
n3:svazekPeriodika
36
n3:tvurceVysledku
Soukenka, Martin Bobok, Jozef
n3:zamer
n17:MSM6840770010
s:issn
0147-1937
s:numberOfPages
14
n20:organizacniJednotka
21110