Irreducibility, Infinite Level Sets,and Small Entropy

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21110%2F11%3A00189602" target="_blank" >RIV/68407700:21110/11:00189602 - isvavai.cz</a>
Result on the web
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DOI - Digital Object Identifier
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Result language
angličtina
Original language name
Irreducibility, Infinite Level Sets,and Small Entropy
Original language 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.
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Project
<a href="/en/project/GA201%2F09%2F0854" target="_blank" >GA201/09/0854: Dynamics of Iterative Systems</a><br>
Continuities
Z - Vyzkumny zamer (s odkazem do CEZ)

Publication year
2011
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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