Bulletin of the London Mathematical Society· 2026Q1
On locally distinguishing Sierpiński dynamical systems
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- Q1SCImago
- 2026year
Short summary
This paper proves no local quasiconformal map exists between the limit set of a convex-cocompact Kleinian group and the Julia set of a postcritically finite rational map, if both are Sierpiński carpets.
AI-generated from the title and abstract; the full text is not read.
Key points
- Proves no local quasiconformal map exists between Sierpiński carpet limit sets of Kleinian groups and Julia sets of rational maps.
- Focuses on the specific case where both fractal sets are Sierpiński carpets.
- Contrasts with prior work that found such maps for gasket and tree-like spaces.
AI-generated from the title and abstract; the full text is not read.
Abstract
Abstract We prove that there is no local quasiconformal map between the limit set of a convex‐cocompact Kleinian group and the Julia set of a postcritically finite rational map, provided that both are Sierpiński carpets. This contrasts with the recent results by Y. Luo, D. Ntalampekos and Y. Luo, M. Mj, S. Mukherjee for gasket and tree‐like spaces, respectively.
The authors' abstract, as published at the source. Bulletin of the London Mathematical Society, 2026 · DOI ↗
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Field: Mathematical Physics
Mathematical PhysicsMathematics