Uniform a priori bounds for neutral renormalization. Variation II: $ψ^\bullet$-ql Siegel maps
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866911186929319936 |
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| author | Dudko, Dzmitry Luo, Yusheng Lyubich, Mikhail |
| author_facet | Dudko, Dzmitry Luo, Yusheng Lyubich, Mikhail |
| contents | We extend uniform pseudo-Siegel bounds for neutral quadratic polynomials to $ψ^\bullet$-quadratic-like Siegel maps. In this form, the bounds are compatible with the $ψ$-quadratic-like renormalization theory and are easily transferable to various families of rational maps. The main theorem states that the degeneration of a Siegel disk is equidistributed among combinatorial intervals. This provides a precise description of how the $ψ^\bullet$-quadratic-like structure degenerates around the Siegel disk on all geometric scales except on the ``transitional scales'' between two specific combinatorial levels. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_23031 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Uniform a priori bounds for neutral renormalization. Variation II: $ψ^\bullet$-ql Siegel maps Dudko, Dzmitry Luo, Yusheng Lyubich, Mikhail Dynamical Systems Complex Variables 30C10, 37F10 We extend uniform pseudo-Siegel bounds for neutral quadratic polynomials to $ψ^\bullet$-quadratic-like Siegel maps. In this form, the bounds are compatible with the $ψ$-quadratic-like renormalization theory and are easily transferable to various families of rational maps. The main theorem states that the degeneration of a Siegel disk is equidistributed among combinatorial intervals. This provides a precise description of how the $ψ^\bullet$-quadratic-like structure degenerates around the Siegel disk on all geometric scales except on the ``transitional scales'' between two specific combinatorial levels. |
| title | Uniform a priori bounds for neutral renormalization. Variation II: $ψ^\bullet$-ql Siegel maps |
| topic | Dynamical Systems Complex Variables 30C10, 37F10 |
| url | https://arxiv.org/abs/2509.23031 |