TY - JOUR
T1 - Likely Limit Sets of a Class of $p$-Order Feigenbaum's Maps
AU - Wang , Wei
AU - Liao , Li
JO - Communications in Mathematical Research 
VL - 2
SP - 137
EP - 145
PY - 2021
DA - 2021/05
SN - 28
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/cmr/19056.html
KW - Feigenbaum's equation, Feigenbaum's map, likely limit set, Hausdorff
dimension.
AB - <p style="text-align: justify;">A continuous map from a closed interval into itself is called a $p$-order
Feigenbaum&#39;s map if it is a solution of the Feigenbaum&#39;s equation $f^p
(λx) = λf(x)$.
In this paper, we estimate Hausdorff dimensions of likely limit sets of some $p$-order
Feigenbaum&#39;s maps. As an application, it is proved that for any $0 &lt; t &lt; 1$, there
always exists a $p$-order Feigenbaum&#39;s map which has a likely limit set with Hausdorff
dimension $t$. This generalizes some known results in the special case of $p = 2$.</p>