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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. (en)
Title
  • Irreducibility, Infinite Level Sets,and Small Entropy
  • Irreducibility, Infinite Level Sets,and Small Entropy (en)
skos:prefLabel
  • Irreducibility, Infinite Level Sets,and Small Entropy
  • Irreducibility, Infinite Level Sets,and Small Entropy (en)
skos:notation
  • RIV/68407700:21110/11:00189602!RIV12-MSM-21110___
http://linked.open...avai/predkladatel
http://linked.open...avai/riv/aktivita
http://linked.open...avai/riv/aktivity
  • P(GA201/09/0854), Z(MSM6840770010)
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
  • 205852
http://linked.open...ai/riv/idVysledku
  • RIV/68407700:21110/11:00189602
http://linked.open...riv/jazykVysledku
http://linked.open.../riv/klicovaSlova
  • interval map, knot point, Lebesgue measure, topological entropy (en)
http://linked.open.../riv/klicoveSlovo
http://linked.open...odStatuVydavatele
  • US - Spojené státy americké
http://linked.open...ontrolniKodProRIV
  • [1596DC5D1AF5]
http://linked.open...i/riv/nazevZdroje
  • Real Analysis Exchange
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
  • 36
http://linked.open...iv/tvurceVysledku
  • Bobok, Jozef
  • Soukenka, Martin
http://linked.open...n/vavai/riv/zamer
issn
  • 0147-1937
number of pages
http://localhost/t...ganizacniJednotka
  • 21110
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