A solution of the Feigenbaum functional equation is called a Feigenbaum map. We investigate the likely limit set (i.e. the maximal attractor in the sense of Milnor) of a non-unimodal Feigenbaum map, prove that it is a minimal set that attracts almost all points, and then estimate its Hausdorff dimension. Finally, for every s ∈ (0,1), we construct a non-unimodal Feigenbaum map with a likely limit set whose Hausdorff dimension is s.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ap110-1-5,
author = {Guifeng Huang and Lidong Wang},
title = {On the attractors of Feigenbaum maps},
journal = {Annales Polonici Mathematici},
volume = {111},
year = {2014},
pages = {55-62},
zbl = {1304.37015},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap110-1-5}
}
Guifeng Huang; Lidong Wang. On the attractors of Feigenbaum maps. Annales Polonici Mathematici, Tome 111 (2014) pp. 55-62. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap110-1-5/