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+ contractions and prove Lebesgue equidistribution under suitable nonlattice and thermodynamic regularity assumptions.
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