@Article{CMR-28-137, author = {Wang , Wei and Liao , Li}, title = {Likely Limit Sets of a Class of $p$-Order Feigenbaum's Maps}, journal = {Communications in Mathematical Research }, year = {2021}, volume = {28}, number = {2}, pages = {137--145}, abstract = {

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 $p = 2$.

}, issn = {2707-8523}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/cmr/19056.html} }