On self-similar dendrites in Hilbert space
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Keywords:
Self-similar set, Open Set Condition, address map, infinitely ramified dendrite, ramification pointsAbstract
We consider the relation of the ramification order of self-similar dendrites in $\mathbb{R}^d$ and in Hilbert space and their Hausdorff dimension and measure.
References
K. Allabergenova, M. Samuel, and A. Tetenov. Intersections of the pieces of selfsimilar dendrites in the plane. Chaos, Solitons & Fractals, 182:114805, 2024.
C. Bandt and S. Graf. Self-similar sets 7. A characterization of self-similar fractals with positive hausdorff measure. Proceedings of the American Mathematical Society, 114(4):995–1001, 1992.
C. Bandt and K. Keller. Self-similar sets 2. A simple approach to the topological structure of fractals. Mathematische Nachrichten, 154(1):27–39, 1991.
C. Bandt and H. Rao. Topology and separation of self-similar fractals in the plane. Nonlinearity, 20(6):1463–1474, May 2007.
C. Bandt and J. Stahnke. Self-similar sets 6. Interior distance on deterministic fractals. Preprint, 1990.
J. J. Charatonik and W. J. Charatonik. Dendrites. Aportaciones Mat. Comun, 22:227–253, 1998.
M. Hata. On the structure of self-similar sets. Japan Journal of Applied Mathematics, 2:381–414, 1985.
J. E. Hutchinson. Fractals and self similarity. Indiana University Mathematics Journal, 30(5):713–747, 1981.
J. Kigami. Harmonic calculus on limits of networks and its application to dendrites. Journal of Functional Analysis, 128(1):48–86, 1995.
J. Kotus and M. Urbański. Meromorphic Dynamics: Abstract Ergodic Theory, Geometry, Graph Directed Markov Systems, and Conformal Measures. Cambridge University Press, 2023.
K. Kuratowski. Topology: Volume II. Elsevier, 2014.
K.-S. Lau and S.-M. Ngai. Multifractal measures and a weak separation condition. Advances in Mathematics, 141(1):45–96, 1999.
A. Schief. Separation properties for self-similar sets. Proceedings of the American Mathematical Society, 122(1):111 115, 1994.
A. Schief. Self-similar sets in complete metric spaces. Proceedings of the American Mathematical Society, 124(2):481-490, 1996.
A. Tetenov. Finiteness properties for self-similar continua. arXiv:2003.04202, 2020.
M. P. W. Zerner. Weak separation properties for self-similar sets. Proceedings of the American Mathematical Society, 124(11):3529–3539, 1996.
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