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arXiv · 2605.16156

A nonlinear version of the $\alpha$-Kakutani equidistribution problem

Ignacio Rojas
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Abstract

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.

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Ignacio Rojas. 2026-05-15. A nonlinear version of the $\alpha$-Kakutani equidistribution problem. https://arxiv.org/abs/2605.16156

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