Year: 2026
Type: preprint
Abstract: We consider smooth symmetric bimodal maps with Fibonacci combinatorics. We prove that, when the critical order is sufficiently large, the common $ω$-limit set of the two critical points is a wild Cantor attractor. Using a full-family argument, we first prove the existence of smooth symmetric Fibonacci bimodal maps with any prescribed critical order $\ell>3$. The proof of the existence of the wild attractor is based on a two-to-one semi-conjugacy which reduces the generalized renormalization of the bimodal map to a Fibonacci box mapping with one critical point.
Source: arXiv (Cornell University)
Author: Ji, Haoyang
Institution: Zhengzhou University
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Award: G1662001357
OpenAlex ID: W7213327013