2017
Том 69
№ 9

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Monotonicity of Topological Entropy for One-Parameter Families of Unimodal Mappings

Volkova O. Yu.

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Abstract

For a special class of one-parameter families of unimodal mappings of the form f t(x): [0, 1] → [0, 1], f t = atx/(x + t), 0 ≤ x ≤ 1/2, we establish that, for t ε [0, 1/(a − 2)], a > 2, the topological entropy h(f t) is a function monotonically increasing in the parameter. We prove that there exists a class of one-parameter families of unimodal mappings f t that contains the family indicated above and establish conditions under which the topological entropy h(f t) is a function monotonically increasing in the parameter.

English version (Springer): Ukrainian Mathematical Journal 55 (2003), no. 11, pp 1733-1741.

Citation Example: Volkova O. Yu. Monotonicity of Topological Entropy for One-Parameter Families of Unimodal Mappings // Ukr. Mat. Zh. - 2003. - 55, № 11. - pp. 1443-1449.

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