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Wild attractor exists for symmetric Fibonacci bimodal map
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 ℓ>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.
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BibTeX
@misc{ji2026wild,
title = {{Wild attractor exists for symmetric Fibonacci bimodal map}},
author = {Haoyang Ji},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.14905},
eprint = {2609.14905},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.14905},
}
RIS
TY - UNPB
TI - Wild attractor exists for symmetric Fibonacci bimodal map
AU - Haoyang Ji
PY - 2026
DA - 2026/09/14
PB - arXiv
DO - 10.48550/arxiv.2609.14905
UR - https://arxiv.org/abs/2609.14905
AB - 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 ℓ>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.
ER -