In a sense that may be made precise, a horocyclic flow is orthogonal to geodesic flows. In that sense this paper is the orthogonal complement of some of the author’s previous work [J. Anal. Math. 39, 1-10 (1981; Zbl 0476.32028)], in which he shows that the (Teichmüller) geodesic flow on the moduli space of stable curves is ergodic. He uses the result and a clever method due to G. A. Hedlung [Ann. Math. (2) 40, 370-383 (1939; Zbl 0020.40302)] to prove the ergodicity of the horocyclic flow on \(Q_ 0/Mod(g)\). Here Mod(g) is the Teichmüller modular group for compact surfaces of genus \(g>1\) and \(Q_ 0\) is the space of unit \(L_ 1\)-norm holomorphic quadratic differentials on compact Riemann surfaces of genus g.
Using these results, it is also shown that Mod(g) acts ergodically on \({\mathcal M}{\mathcal F}\), the space of equivalence classes of measured foliations on surfaces of genus g. The equivalence relation is modulo isotopy and Whitehead moves as is standard in the Thurston theory.