Volume 28, Issue 2
Likely Limit Sets of a Class of $p$-Order Feigenbaum's Maps

Commun. Math. Res., 28 (2012), pp. 137-145.

Published online: 2021-05

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• 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 $p = 2$.

• Keywords

Feigenbaum's equation, Feigenbaum's map, likely limit set, Hausdorff dimension.

39B52

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@Article{CMR-28-137, author = {Wei and Wang and and 18480 and and Wei Wang and Li and Liao and and 18481 and and Li Liao}, 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} }
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 -

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 $p = 2$.

Wei Wang & Li Liao. (2021). Likely Limit Sets of a Class of $p$-Order Feigenbaum's Maps. Communications in Mathematical Research . 28 (2). 137-145. doi:
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