Work

A NEW PROOF OF THE SINGULAR CONTINUITY OF THE MINKOWSKI question mark $?$ ? -FUNCTION

Year: 2025

Type: article

Abstract: We give a new proof of the singular continuity of Minkowski’s question mark $?$ ? -function. Our proof follows by showing that the maximal Lyapunov exponent of a specific pair of 3 times 3 $3\times 3$ 3 × 3 nonnegative integer matrices related to Stern’s diatomic sequence is strictly greater than log 2 $\log 2$ log 2 .

Source: Bulletin of the Australian Mathematical Society

DOI: 10.1017/s0004972725100701

Authors: MICHAEL COONS, SAMUEL COYLE, ARI PINCUS KAZMAR, ADAM STOUT, DYLAN WOOD

Institutions: California State University System, California State University, Chico, University of Minnesota, Macalester College

Language: English

Topic: Mathematical Dynamics and Fractals

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $3,550

Funder: National Science Foundation