PreprintCC BY-NC-SA 4.0arXiv
A nonlinear version of the α-Kakutani equidistribution problem
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 𝒞1+ ε contractions and prove Lebesgue equidistribution under suitable nonlattice and thermodynamic regularity assumptions.
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BibTeX
@misc{rojas2026nonlinear,
title = {{A nonlinear version of the $α$-Kakutani equidistribution problem}},
author = {Ignacio Rojas},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2605.16156},
eprint = {2605.16156},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.16156},
note = {CC BY-NC-SA 4.0},
}
RIS
TY - UNPB
TI - A nonlinear version of the α-Kakutani equidistribution problem
AU - Ignacio Rojas
PY - 2026
DA - 2026/10/16
PB - arXiv
DO - 10.48550/arxiv.2605.16156
UR - https://arxiv.org/abs/2605.16156
AB - 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 𝒞^1+ ε contractions and prove Lebesgue equidistribution under suitable nonlattice and thermodynamic regularity assumptions.
ER -