Abstract
We formulate the weak separation condition and the finite type condition for conformal iterated function systems on Riemannian manifolds with nonnegative Ricci curvature, and generalize the main theorems by Lau et al. (Monatsch Math 156:325–355, 2009). We also obtain a formula for the Hausdorff dimension of a self-similar set defined by an iterated function system satisfying the finite type condition, generalizing a corresponding result by Jin and Yau (Commun Anal Geom 13:821–843, 2005) and Lau and Ngai (Adv Math 208:647–671, 2007) on Euclidean spaces. Moreover, we obtain a formula for the Hausdorff dimension of a graph self-similar set generated by a graph-directed iterated function system satisfying the graph finite type condition, extending a result by Ngai et al. (Nonlinearity 23:2333–2350, 2010).
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Acknowledgements
The authors are supported in part by the National Natural Science Foundation of China, Grants 11771136 and 12271156, and Construct Program of the Key Discipline in Hunan Province. The first author is also supported in part by a Faculty Research Scholarly Pursuit Funding from Georgia Southern University. The second author is also supported in part by the National Natural Science Foundation of China, grant 11771391 and the Fundamental Research Funds for the Central Universities of China grant 2021FZZX001-01.
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Ngai, SM., Xu, Y. Separation Conditions for Iterated Function Systems with Overlaps on Riemannian Manifolds. J Geom Anal 33, 262 (2023). https://doi.org/10.1007/s12220-023-01318-6
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DOI: https://doi.org/10.1007/s12220-023-01318-6