(untitled) (Communications in Mathematical Research, 2021)
A continuous map from a closed interval into itself is called a p-order Feigenbaum's map if it is a solution of the Feigenbaum's equation f^p (λx) = λf(x). In this paper, we estimate Hausdorff dimensions of likely limit sets of some p-order Feigenbaum's maps. As an application, it is proved that for any 0 < t < 1, there always exists a p-order Feigenbaum's map which has a likely limit set with Hausdorff dimension t. This generalizes some known results in the special case of p = 2.