Slicing the Torus and the thermodynamics of self-similar measures with overlaps
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866912993841774592 |
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| author | Ingarfield, Peej |
| author_facet | Ingarfield, Peej |
| contents | Orthogonal projections of the uniform measure on the Sierpinski triangle form a family of self similar measures with overlaps. The main result of this work is to make a connection between the dimension theory of these measures and the thermodynamic formalism of the doubling map restricted to rational slices of the torus. Of note is how we establish a correspondence between the varying translational parameter and varying rational slices. This gives a new direction from which to understand the dimension theory of projections of self similar measures. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_17145 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Slicing the Torus and the thermodynamics of self-similar measures with overlaps Ingarfield, Peej Dynamical Systems Orthogonal projections of the uniform measure on the Sierpinski triangle form a family of self similar measures with overlaps. The main result of this work is to make a connection between the dimension theory of these measures and the thermodynamic formalism of the doubling map restricted to rational slices of the torus. Of note is how we establish a correspondence between the varying translational parameter and varying rational slices. This gives a new direction from which to understand the dimension theory of projections of self similar measures. |
| title | Slicing the Torus and the thermodynamics of self-similar measures with overlaps |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2502.17145 |