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| Formato: | Preprint |
| Publicado: |
2026
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| Acceso en línea: | https://arxiv.org/abs/2605.19097 |
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| _version_ | 1866913175523295232 |
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| author | Chandra, Subhash |
| author_facet | Chandra, Subhash |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_19097 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Some topological properties and bi-Lipschitz equivalence of graph-directed attractors Chandra, Subhash Dynamical Systems 28A80, 05C20 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. |
| title | Some topological properties and bi-Lipschitz equivalence of graph-directed attractors |
| topic | Dynamical Systems 28A80, 05C20 |
| url | https://arxiv.org/abs/2605.19097 |