On the Global Curve Attractor for polynomial gluing
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866909008069132288 |
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| author | Wu, Panjing |
| author_facet | Wu, Panjing |
| contents | Pilgrim's Finite Global Attractor Conjecture has been verified for polynomials [1], but remains open for general rational maps. In this paper, we prove the conjecture for a family of rational maps obtained by gluing two PCF polynomials along the boundaries of their finite superattracting basins. Adapting the idea of [17], we show that a suitably defined intersection number with a finite family of separating arcs eventually decays under pullback, yielding a finite collection of homotopy classes that attracts all non-peripheral curves under iteration. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_00633 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On the Global Curve Attractor for polynomial gluing Wu, Panjing Dynamical Systems Pilgrim's Finite Global Attractor Conjecture has been verified for polynomials [1], but remains open for general rational maps. In this paper, we prove the conjecture for a family of rational maps obtained by gluing two PCF polynomials along the boundaries of their finite superattracting basins. Adapting the idea of [17], we show that a suitably defined intersection number with a finite family of separating arcs eventually decays under pullback, yielding a finite collection of homotopy classes that attracts all non-peripheral curves under iteration. |
| title | On the Global Curve Attractor for polynomial gluing |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2605.00633 |