Work

Convergence and combinatorics of the Reverse algorithm

Year: 2026

Type: article

Abstract: We study the Reverse algorithm, a multidimensional continued fraction algorithm, which is not unimodular. We show that the Reverse algorithm is ergodic and, by proving that its second Lyapunov exponent is negative, that it is a.e. exponentially convergent. In addition to that, we attach substitutions to this algorithm and study the ‐adic languages generated by sequences of these substitutions. The negativity of the second Lyapunov exponent implies that almost all of these languages are balanced. By a thorough study of the combinatorics of the substitutions, we are even able to obtain a concrete generic family of balanced languages that is characterized in terms of a simple condition on the underlying sequence of substitutions.

Source: Bulletin of the London Mathematical Society

DOI: 10.1112/blms.70470

Authors: Hiroaki Ito, Niels Langeveld, Jörg Thuswaldner

Institution: Montanuniversität Leoben

Language: English

Topic: Mathematical Dynamics and Fractals

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,930

Funders: Agence Nationale de la Recherche, Austrian Science Fund