Geodesic
Application of kneading series to semiconjugacy of Lorenz maps of zero entropy
Žurnal Srednevolžskogo matematičeskogo obŝestva, Tome 18 (2016) no. 4, pp. 34-40

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For one-dimensional discontinuous maps of Lorenz type with zero topological entropy, we apply the technique of kneading invariants and kneading series. The kneading technique was introduced first by J. Milnor and W. Thurston for continuous piecewise-monotone one-dimensional maps and was applied to maps with positive topological entropy. In present paper we show that by approaching the zero entropy one may (using kneading series) define invariant measure for Lorenz maps under consideration. Thus one may construct semiconjugacy (being actually a conjugacy in the transitive case) with a model map of unit slope.
Keywords: topological entropy, Lorenz type maps, kneading invariants. 
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     author = {M. I. Malkin and K. A. Saphonov},
     title = {Application of kneading series to semiconjugacy of {Lorenz} maps of zero entropy},
     journal = {\v{Z}urnal Srednevol\v{z}skogo matemati\v{c}eskogo ob\^{s}estva},
     pages = {34--40},
     publisher = {mathdoc},
     volume = {18},
     number = {4},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SVMO_2016_18_4_a3/}
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M. I. Malkin; K. A. Saphonov. Application of kneading series to semiconjugacy of Lorenz maps of zero entropy. Žurnal Srednevolžskogo matematičeskogo obŝestva, Tome 18 (2016) no. 4, pp. 34-40. http://geodesic.mathdoc.fr/item/SVMO_2016_18_4_a3/