Pseudo-monodromy and the Mandelbrot set
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866912437033238528 |
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| author | Ishii, Yutaka Richards, Thomas |
| author_facet | Ishii, Yutaka Richards, Thomas |
| contents | We investigate the discontinuity of codings for the Julia set of a quadratic map. To each parameter ray, we associate a natural coding for Julia sets on the ray. Given a hyperbolic component $H$ of the Mandelbrot set, we consider the codings along the two parameter rays landing on the root point of $H$. Our main result describes the discontinuity of these two codings in terms of the kneading sequences of the hyperbolic components which are conspicuous to $H$. This result can be interpreted as a solution to the degenerate case of the monodromy action conjecture in the horseshoe locus for the complex Hénon family. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_02204 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Pseudo-monodromy and the Mandelbrot set Ishii, Yutaka Richards, Thomas Dynamical Systems Primary 37F20, 37F46, Secondary 37F80 We investigate the discontinuity of codings for the Julia set of a quadratic map. To each parameter ray, we associate a natural coding for Julia sets on the ray. Given a hyperbolic component $H$ of the Mandelbrot set, we consider the codings along the two parameter rays landing on the root point of $H$. Our main result describes the discontinuity of these two codings in terms of the kneading sequences of the hyperbolic components which are conspicuous to $H$. This result can be interpreted as a solution to the degenerate case of the monodromy action conjecture in the horseshoe locus for the complex Hénon family. |
| title | Pseudo-monodromy and the Mandelbrot set |
| topic | Dynamical Systems Primary 37F20, 37F46, Secondary 37F80 |
| url | https://arxiv.org/abs/2405.02204 |