Abstract
We are interested in the Julia set of a semigroup of rational functions with coefficients in $\mathbb{C}_p$ where the semigroup operation is composition. We prove that if a semigroup $G$ is generated by a finite number of rational functions of degree at least two with coefficients in a finite extension of $\mathbb{Q}_p$, and has a nonempty Julia set $\mathcal{J}(G)$, then $\mathcal{J}(G)$ is perfect and has an empty interior.
Citation
Abdelaziz Bellagh. "SEMIGROUP OF RATIONAL $p$-ADIC FUNCTIONS FOR COMPOSITION." Taiwanese J. Math. 14 (4) 1385 - 1409, 2010. https://doi.org/10.11650/twjm/1500405955
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