Application of kneading series to semiconjugacy of Lorenz maps of zero entropy
M. Malkin1, K. Safonov2
| Annotation | 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. |
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| Keywords | topological entropy, Lorenz type maps, kneading invariants |
1Associate professor of Department of Differential Equations, Mathematical and Numerical Analysis,Lobachevsky State University, Nizhny Novgorod; malkin@unn.ru
2Student, Lobachevsky State University, Nizhny Novgorod
Citation: M. Malkin, K. Safonov, "[Application of kneading series to semiconjugacy of Lorenz maps of zero entropy]", Zhurnal Srednevolzhskogo matematicheskogo obshchestva,18:4 (2016) 34–40 (In Russian)
