Year: 2012
Communications in Mathematical Research , Vol. 28 (2012), Iss. 2 : pp. 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 $p = 2$.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2012-CMR-19056
Communications in Mathematical Research , Vol. 28 (2012), Iss. 2 : pp. 137–145
Published online: 2012-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 9
Keywords: Feigenbaum's equation Feigenbaum's map likely limit set Hausdorff dimension.