A nonlinear version of the $\alpha$-Kakutani equidistribution problem
Dynamical Systems
2026-05-29 v2
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 contractions and prove Lebesgue equidistribution under suitable nonlattice and thermodynamic regularity assumptions.
Cite
@article{arxiv.2605.16156,
title = {A nonlinear version of the $\alpha$-Kakutani equidistribution problem},
author = {Ignacio Rojas},
journal= {arXiv preprint arXiv:2605.16156},
year = {2026}
}
Comments
Added my email address at the end and a comment in Example 4.1