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

• Date: 2003
• Main Authors: Volkova, O. Yu., Волкова, О. Ю.
• Format: Article
• Language: Russian; English
• Published: Institute of Mathematics, NAS of Ukraine 2003
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/4014
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

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...