2026/05/31 by Pierre Arnoux, Thomas A. Schmidt
Mathematics · Physics and Astronomy · #Ergodic theory #Flow (mathematics) #Geodesic #Geodesic flow #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #Modular design #Quantum chaos and dynamical systems #Sketch #Surface (topology) #Symbolic dynamics
paper · doi:10.1112/jlms.70588
openalex publication_date 2026/07/01 · openalex created_date 2026/07/04 · openalex updated_date 2026/07/04
Abstract Caroline Series' [ The modular surface and continued fractions , J. Lond. Math. Soc. (2), 31 , no. 1, (1985), 69–80] gives a clear framework linking, in a deceptively simple way, the dynamics of the geodesic flow on the modular surface with the dynamics of the regular continued fraction, through a well‐chosen symbolic coding. It has been called required reading for those interested in the symbolic dynamics of geodesic flows, and has had consequences in symbolic dynamics, ergodic theory, hyperbolic geometry, and continued fraction theory. In this overview, we give an indication of why this is so, sketch some of the history related to the paper, and also point to some later works.