On the Hausdorff dimension of invariant measures of piecewise smooth circle homeomorphisms
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866912124885794816 |
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| author | Trujillo, Frank |
| author_facet | Trujillo, Frank |
| contents | We show that, generically, the unique invariant measure of a sufficiently regular piecewise smooth circle homeomorphism with irrational rotation number and zero mean nonlinearity (e.g., piecewise linear) has zero Hausdorff dimension.
To encode this generic condition, we consider piecewise smooth homeomorphisms as generalized interval exchange transformations (GIETs) of the interval and rely on the notion of combinatorial rotation number for GIETs, which can be seen as an extension of the classical notion of rotation number for circle homeomorphisms to the GIET setting. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2210_16233 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | On the Hausdorff dimension of invariant measures of piecewise smooth circle homeomorphisms Trujillo, Frank Dynamical Systems We show that, generically, the unique invariant measure of a sufficiently regular piecewise smooth circle homeomorphism with irrational rotation number and zero mean nonlinearity (e.g., piecewise linear) has zero Hausdorff dimension. To encode this generic condition, we consider piecewise smooth homeomorphisms as generalized interval exchange transformations (GIETs) of the interval and rely on the notion of combinatorial rotation number for GIETs, which can be seen as an extension of the classical notion of rotation number for circle homeomorphisms to the GIET setting. |
| title | On the Hausdorff dimension of invariant measures of piecewise smooth circle homeomorphisms |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2210.16233 |