2017/04/23 by A. Muhammed Uludağ, Uludağ, Muhammed, Hakan Ayral +1
Mathematics · Physics and Astronomy · #11A55 #11K50 #Advanced Differential Equations and Dynamical Systems #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems
paper · pdf · doi:10.48550/arxiv.1704.06912
openalex publication_date 2017/04/23 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28
We study the dynamics of a family of continued fraction maps parametrized by the unit interval. This family contains as special instances the Gauss continued fraction map and the Fibonacci map. We determine the transfer operators of these dynamical maps and make a preliminary study of them. We show that their analytic invariant measures obeys a common functional equation generalizing Lewis' functional equation and we find invariant measures for some members of the family. We also discuss a certain involution of this family which sends the Gauss map to the Fibonacci map.