Uniform a priori bounds for neutral renormalization
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866912170765189120 |
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| author | Dudko, Dzmitry Lyubich, Mikhail |
| author_facet | Dudko, Dzmitry Lyubich, Mikhail |
| contents | We prove uniform ``pseudo-Siegel'' a priori bounds for Siegel disks of bounded type that give a uniform control of oscillations of their boundaries in all scales. As a consequence, we construct the Mother Hedgehog controlling the postcritical set for any quadratic polynomial with a neutral periodic point and show that this hedgehog has a star-like structure. Pseudo-Siegel bounds imply uniform a priori bounds of the Sector Renormalization, which gives an opportunity to extend Siegel/Pacman Renormalization Theory and Near-Parabolic Renormalization Theory to all near-neutral quadratic polynomials. Various applications beyond quadratic polynomials are also underway. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2210_09280 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Uniform a priori bounds for neutral renormalization Dudko, Dzmitry Lyubich, Mikhail Dynamical Systems We prove uniform ``pseudo-Siegel'' a priori bounds for Siegel disks of bounded type that give a uniform control of oscillations of their boundaries in all scales. As a consequence, we construct the Mother Hedgehog controlling the postcritical set for any quadratic polynomial with a neutral periodic point and show that this hedgehog has a star-like structure. Pseudo-Siegel bounds imply uniform a priori bounds of the Sector Renormalization, which gives an opportunity to extend Siegel/Pacman Renormalization Theory and Near-Parabolic Renormalization Theory to all near-neutral quadratic polynomials. Various applications beyond quadratic polynomials are also underway. |
| title | Uniform a priori bounds for neutral renormalization |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2210.09280 |