Smooth Circle Covering with a Physical Measure on a Hyperbolic Repelling Fixed Point
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866908965654233088 |
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| author | Gunawan, Rubio |
| author_facet | Gunawan, Rubio |
| contents | We construct an example of a smooth ($C^\infty$) circle covering map topologically conjugate to the doubling map, such that it has a physical measure supported on a hyperbolic repelling fixed point. By relaxing the smooth condition at a single point, we also construct an example where the basin of the physical measure has full measure. A key technical step is a realization method of independent interest, which gives a canonical way to construct a full branch map given its induced map. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_00293 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Smooth Circle Covering with a Physical Measure on a Hyperbolic Repelling Fixed Point Gunawan, Rubio Dynamical Systems 37E10 We construct an example of a smooth ($C^\infty$) circle covering map topologically conjugate to the doubling map, such that it has a physical measure supported on a hyperbolic repelling fixed point. By relaxing the smooth condition at a single point, we also construct an example where the basin of the physical measure has full measure. A key technical step is a realization method of independent interest, which gives a canonical way to construct a full branch map given its induced map. |
| title | Smooth Circle Covering with a Physical Measure on a Hyperbolic Repelling Fixed Point |
| topic | Dynamical Systems 37E10 |
| url | https://arxiv.org/abs/2602.00293 |