**MSC2010** 37E05

### Niding designs of models of constant inclination for generalized shifts of a segment

#### M. Malkin^{1}, K. Safonov^{2}

Annotation | For one-dimensional discontinuous maps 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 the present paper we show that by approaching the zero entropy, with the help of kneading series one may define invariant measure for generalized interval exchange transformations and also for a class of discontinuous maps without periodic points. Thus, we construct in terms of the kneading series a semiconjugacy (being actually a conjugacy in the transitive case) with a model map of unit (in absolute value) slope. The proposed construction is determined by formulas which allow to calculate with required accuracy, the parameters of the model map. |
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Keywords | topological entropy, Lorenz type maps, kneading invariant |

^{1}**Mihail I. Malkin**, Associate Professor of the Department of Differential Equations, Mathematical and Numerical Analysis, Institute of Information Technologies, Mathematics and Mechanics, FGAOU VO "National research Nizhny Novgorod State University. N. I. Lobachevsky", (603950, Russia, GSP-20, Nizhny Novgorod, 23 Gagarin Av., building 6), Ph.D. (Physics and Mathematics), ORCID:http://orsid.org/0000-0002-1233-0264, malkin@mm.unn.ru^{2}**Klim A. Safonov**, student, Institute of Information Technologies, Mathematics and Mechanics, FGAOU VO "National research Nizhny Novgorod State University. N. I. Lobachevsky", (603950, Russia, GSP-20, Nizhny Novgorod, 23 Gagarin Av., building 6), ORCID:http://orсid.org/0000-0001-8623-4294, safonov.klim@yandex.ru

**Citation**: M. Malkin, K. Safonov, "[Niding designs of models of constant inclination for generalized shifts of a segment]", Zhurnal Srednevolzhskogo matematicheskogo obshchestva,19:2 (2017) 85–90 (In Russian)

**DOI** 10.15507/2079-6900.19.201701.085-090