A criterion for the simplicity of the Lyapunov spectrum of square-tiled surfaces

作者：Matheus Carlos^*; Moeller Martin; Yoccoz Jean Christophe

来源：Inventiones Mathematicae, 2015, 202(1): 333-425.

DOI：10.1007/s00222-014-0565-5

We present a Galois-theoretical criterion for the simplicity of the Lyapunov spectrum of the Kontsevich-Zorich cocycle over the Teichmuller flow on the -orbit of a square-tiled surface. The simplicity of the Lyapunov spectrum has been proved by A. Avila and M. Viana with respect to the so-called Masur-Veech measures associated to connected components of moduli spaces of translation surfaces, but is not always true for square-tiled surfaces of genus . We apply our criterion to square-tiled surfaces of genus 3 with one single zero. Conditionally to a conjecture of Delecroix and LeliSvre, we prove with the aid of Siegel's theorem (on integral points on algebraic curves of genus ) that all but finitely many such square-tiled surfaces have simple Lyapunov spectrum.

• 出版日期2015-10