Multi-modal-extended solutions of the Feigenbaum equation

[摘要] The Feigenbaum equation describes universal features of period-doubling in interval maps. Based on the known result on existence of continuous solutions, efforts have been made to find specific classes of continuous solutions, which exhibit structure of various continuous solutions. In addition to solutions of simpler structure such as bijective solutions, some non-monotonic solutions such as unimodal solutions and unimodal-extended solutions were obtained. In this paper we find a new and more complicated class of solutions, called multi-modal-extended solutions, and illustrate their structure with 2-modal-extended solutions. Furthermore, we give conditions to guarantee smoothness of those solutions. (C) 2019 Elsevier Inc. All rights reserved.

[发布日期] 2019-12-01

[关键词] Feigenbaum equation;Iterative construction method;Multi-modal-extended solution;C-k solution