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arXiv · 2605.19097

Some topological properties and bi-Lipschitz equivalence of graph-directed attractors

Subhash Chandra
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Abstract

In this paper, we discuss some topological properties of the graph-directed iterated function system (GDIFS) of injective contractions. Further, we establish the existence of a Lipschitz bijection between two different bi-Lipschitz graph-directed attractors. In general, two different bi-Lipschitz graph-directed attractors defined on the same graph need not be bi-Lipschitz equivalent. However, under suitable conditions, we prove that these graph-directed attractors are bi-Lipschitz equivalent.

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Subhash Chandra. 2026-05-18. Some topological properties and bi-Lipschitz equivalence of graph-directed attractors. https://arxiv.org/abs/2605.19097

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