Continuity of topological entropy for piecewise smooth Lorenz type mappings
M. Malkin1, K. Safonov2
| Annotation | For one-dimensional mappings of Lorenz type, the problem on behavior of the topological entropy as the function of a mapping is studied. In the previous paper the authors proved that entropy as the function of a mapping with $C^0$-topology can have jumps only for exceptional case, namely, in a neighbourhood of a mapping with zero entropy, and moreover, if and only if two kneading invariants are periodic with the same period. In the present paper we show that for the class of Lorenz mappings having zero one-sided derivatives at the discontinuity point and with $C^1$-topology, such an exceptional case is impossible, and thus the entropy depends continously on the mapping. |
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| Keywords | topological entropy, Lorenz type mappings, kneading invariant |
1Associate professor of the Department of differential equations, mathematical and numerical analysis, Lobachevsky State University of Nizhny Novgorod, Institute of Information Technology, Mathematics and Mechanics, Nizhny Novgorod; malkin@unn.ru
2Student, Lobachevsky State University of Nizhny Novgorod, Institute of Information Technology, Mathematics and Mechanics, Nizhny Novgorod
Citation: M. Malkin , K. Safonov, "[Continuity of topological entropy for piecewise smooth Lorenz type mappings]", Zhurnal Srednevolzhskogo matematicheskogo obshchestva,18:2 (2016) 59–66 (In Russian)
