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ISSN (Print) 2079-6900

ISSN (Online) 2587-7496

(Middle Volga Mathematical Society Journal)

Scientific Journal

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Accurate assessment of the topological entropy for breaks maps of Lorenz type

M. Malkin1, K. Saphonov2

AnnotationFor 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.
Keywordstopological 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)