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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2312.17405 |
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| _version_ | 1866911944970076160 |
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| author | Cockram, Noah Ashwin, Peter Rodrigues, Ana |
| author_facet | Cockram, Noah Ashwin, Peter Rodrigues, Ana |
| contents | In this paper, we investigate a class of non-invertible piecewise isometries on the upper half-plane known as Translated Cone Exchanges. These maps include a simple interval exchange on a boundary we call the baseline. We provide a geometric construction for the first return map to a neighbourhood of the vertex of the middle cone for a large class of parameters, then we show a recurrence in the first return map tied to Diophantine properties of the parameters, and subsequently prove the infinite renormalizability of the first return map for these parameters. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_17405 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Renormalization of Translated Cone Exchange Transformations Cockram, Noah Ashwin, Peter Rodrigues, Ana Dynamical Systems 37E20 In this paper, we investigate a class of non-invertible piecewise isometries on the upper half-plane known as Translated Cone Exchanges. These maps include a simple interval exchange on a boundary we call the baseline. We provide a geometric construction for the first return map to a neighbourhood of the vertex of the middle cone for a large class of parameters, then we show a recurrence in the first return map tied to Diophantine properties of the parameters, and subsequently prove the infinite renormalizability of the first return map for these parameters. |
| title | Renormalization of Translated Cone Exchange Transformations |
| topic | Dynamical Systems 37E20 |
| url | https://arxiv.org/abs/2312.17405 |