Accurate assessment of the topological entropy for breaks maps of Lorenz type
M. Malkin1, K. Saphonov2
| Annotation | For one-dimensional maps of Lorenz type, the problem on behavior of the topological entropy as the function of a map is studied. Using the technique of symbolic dynamics (the kneading technique) and by renormalization arguments we show that the topological entropy can have jumps only in a neighbourhood of a map with zero entropy, and moreover, such a jump appear if and only if two kneadind invariants are repiodic with the same period. An exact estimate on the value of the jump for this case is given. |
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| Keywords | topological Markov chains, topological entropy, Lorenz type maps |
1Associate Professor of Department of differential equations and mathematical Analysis, Nizhny Novgorod State University. N. I. Lobachevsky; malkin@mm.unn.ru
2Student of Institute of Information Technology, Mathematics and Mechanics, Nizhny Novgorod State University. N.I. Lobachevsky, Nizhny Novgorod; malkin@mm.unn.ru
Citation: M. Malkin , K. Saphonov, "[Accurate assessment of the topological entropy for breaks maps of Lorenz type]", Zhurnal Srednevolzhskogo matematicheskogo obshchestva,17:4 (2015) 31–36 (In Russian)
