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Solutions for the $p$-order Feigenbaum's functional equation $h(g(x))=g^{p}(h(x))$

Tom 111 / 2014

Min Zhang, Jianguo Si Annales Polonici Mathematici 111 (2014), 183-195 MSC: 39B12. DOI: 10.4064/ap111-2-6

Streszczenie

This work deals with Feigenbaum's functional equation $$\left\{ \begin{array}{l} h(g(x))=g^p(h(x)),\\ g(0)=1, \quad -1\leq g(x)\leq1 ,\quad x\in[-1,1], \end{array} \right. $$ where $p\geq 2$ is an integer, $g^p$ is the $p$-fold iteration of $g$, and $h$ is a strictly monotone odd continuous function on $[-1,1]$ with $h(0)=0$ and $|h(x)|<|x|$ ($x\in[-1,1]$, $x\neq 0$). Using a constructive method, we discuss the existence of continuous unimodal even solutions of the above equation.

Autorzy

  • Min ZhangSchool of Science
    China University of Petroleum
    266555 Qingdao, Shandong
    People's Republic of China
    e-mail
  • Jianguo SiSchool of Mathematics
    Shandong University
    250100 Jinan, Shandong
    People's Republic of China

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