Substitutions and M\"obius disjointness
S. Ferenczi, J. Ku{\l}aga-Przymus, M. Lema\'nczyk, C. Mauduit
TL;DR
This paper proves Sarnak's conjecture on M"obius disjointness for specific dynamical systems, including bijective substitutions and sequences like Rudin-Shapiro, expanding the classes of systems where the conjecture holds.
Contribution
It establishes the validity of Sarnak's conjecture for new classes of dynamical systems, notably bijective substitutions and related sequences.
Findings
Sarnak's conjecture holds for bijective substitution systems
The conjecture is verified for systems generated by Rudin-Shapiro type sequences
The results extend the scope of M"obius disjointness in dynamical systems
Abstract
We show that Sarnak's conjecture on M\"obius disjointness holds for all subshifts given by bijective substitutions and some other similar dynamical systems, e.g.\ those generated by Rudin-Shapiro type sequences.
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Taxonomy
Topicssemigroups and automata theory · Advanced Mathematical Identities · Advanced Combinatorial Mathematics