2013/12/08 by Christopher J. Leininger, Leininger, Christopher, Anna Lenzhen +3
Mathematics · #32G15 (Primary) #37A25 #57M50 (Secondary) #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals
paper · pdf · doi:10.48550/arxiv.1312.2305
openalex publication_date 2013/12/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
We describe a method for constructing Teichm "uller geodesics where the\nvertical measured foliation \ν is minimal but is not uniquely ergodic and\nwhere we have a good understanding of the behavior of the Teichm "uller\ngeodesic. The construction depends on various parameters, and we show that one\ncan adjust the parameters to ensure that the set of accumulation points of such\na geodesic in the Thurston boundary is exactly the set of all possible measured\nfoliations in the homotopy class of \ν. With further adjustment of the\nparameters, one can even take \ν to be an ergodic measure on a non-uniquely\nergodic foliation.\n