A nonlinear version of the $α$-Kakutani equidistribution problem
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866913170404147200 |
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| author | Rojas, Ignacio |
| author_facet | Rojas, Ignacio |
| contents | In this work, we extend results of Kakutani; Adler and Flatto; Smilansky; Pollicott and Sewell on the equidistribution of endpoints generated by interval-splitting procedures. We study a nonlinear version of the problem generated by a finite or countable family of $\mathcal{C}^{1+ \varepsilon}$ contractions and prove Lebesgue equidistribution under suitable nonlattice and thermodynamic regularity assumptions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_16156 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A nonlinear version of the $α$-Kakutani equidistribution problem Rojas, Ignacio Dynamical Systems In this work, we extend results of Kakutani; Adler and Flatto; Smilansky; Pollicott and Sewell on the equidistribution of endpoints generated by interval-splitting procedures. We study a nonlinear version of the problem generated by a finite or countable family of $\mathcal{C}^{1+ \varepsilon}$ contractions and prove Lebesgue equidistribution under suitable nonlattice and thermodynamic regularity assumptions. |
| title | A nonlinear version of the $α$-Kakutani equidistribution problem |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2605.16156 |