Mobius disjointness for interval exchange transformations on three intervals

TL;DR

This paper proves that Sarnak's conjecture on Mobius disjointness applies to a specific class of interval exchange transformations on three intervals, under a mild diophantine condition, advancing understanding in dynamical systems.

Contribution

It establishes Mobius disjointness for 3-interval exchange transformations satisfying a mild diophantine condition, a new result in the field.

Findings

Mobius disjointness proven for 3-IETs under diophantine conditions

Advances understanding of number-theoretic properties in dynamical systems

Supports Sarnak's conjecture in a new class of transformations

Abstract

We show that Sarnak's conjecture on Mobius disjointness holds for interval exchange transformations on three intervals (3-IETs) that satisfy a mild diophantine condition.