Master Teapots and Entropy Algorithms for the Mandelbrot Set
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2021
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| _version_ | 1866915026505302016 |
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| author | Lindsey, Kathryn Tiozzo, Giulio Wu, Chenxi |
| author_facet | Lindsey, Kathryn Tiozzo, Giulio Wu, Chenxi |
| contents | We construct an analogue of W. Thurston's "Master teapot" for each principal vein in the Mandelbrot set, and generalize geometric properties known for the corresponding object for real maps. In particular, we show that eigenvalues outside the unit circle move continuously, while we show "persistence" for roots inside the unit circle. As an application, this shows that the outside part of the corresponding "Thurston set" is path connected. In order to do this, we define a version of kneading theory for principal veins, and we prove the equivalence of several algorithms that compute the core entropy. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2112_14590 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Master Teapots and Entropy Algorithms for the Mandelbrot Set Lindsey, Kathryn Tiozzo, Giulio Wu, Chenxi Dynamical Systems Geometric Topology 37F20, 37F46, 37B40 We construct an analogue of W. Thurston's "Master teapot" for each principal vein in the Mandelbrot set, and generalize geometric properties known for the corresponding object for real maps. In particular, we show that eigenvalues outside the unit circle move continuously, while we show "persistence" for roots inside the unit circle. As an application, this shows that the outside part of the corresponding "Thurston set" is path connected. In order to do this, we define a version of kneading theory for principal veins, and we prove the equivalence of several algorithms that compute the core entropy. |
| title | Master Teapots and Entropy Algorithms for the Mandelbrot Set |
| topic | Dynamical Systems Geometric Topology 37F20, 37F46, 37B40 |
| url | https://arxiv.org/abs/2112.14590 |