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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2603.12877 |
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| _version_ | 1866915859330498560 |
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| author | Dajani, Karma Langeveld, Niels |
| author_facet | Dajani, Karma Langeveld, Niels |
| contents | We characterize all pairs $(β,n),(β^\prime,m)$ such that the alternate $(β,n)$ and $(β^\prime,m)$-transformations $K_{(β,n)}$ and $K_{(β^\prime,m)}$ have the same absolutely continuous invariant measure, where $K_{(β,n)}(i,x)=(i+1 \mod 2 ,T_i(x))$ with $i\in\{0,1\}$, $T_0(x)=T_β(x)=βx \mod 1$, $T_1(x)=T_n(x)=nx\mod 1$ with $β>1$ real and $n\geq 2$ an integer. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_12877 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Coincidence of invariant measure for the alternate base transformations Dajani, Karma Langeveld, Niels Dynamical Systems 11A63, 37A44, 28D05 We characterize all pairs $(β,n),(β^\prime,m)$ such that the alternate $(β,n)$ and $(β^\prime,m)$-transformations $K_{(β,n)}$ and $K_{(β^\prime,m)}$ have the same absolutely continuous invariant measure, where $K_{(β,n)}(i,x)=(i+1 \mod 2 ,T_i(x))$ with $i\in\{0,1\}$, $T_0(x)=T_β(x)=βx \mod 1$, $T_1(x)=T_n(x)=nx\mod 1$ with $β>1$ real and $n\geq 2$ an integer. |
| title | Coincidence of invariant measure for the alternate base transformations |
| topic | Dynamical Systems 11A63, 37A44, 28D05 |
| url | https://arxiv.org/abs/2603.12877 |