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

  • O. Yu. Volkova

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.
Published
25.11.2003
How to Cite
Volkova, O. Y. “Monotonicity of Topological Entropy for One-Parameter Families of Unimodal Mappings”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 55, no. 11, Nov. 2003, pp. 1443-9, https://umj.imath.kiev.ua/index.php/umj/article/view/4014.
Section
Research articles