English

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 C1+ε\mathcal{C}^{1+ \varepsilon} contractions and prove Lebesgue equidistribution under suitable nonlattice and thermodynamic regularity assumptions.

Keywords

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

R2 v1 2026-07-22T07:14:54.982Z