Simplicity of the Lyapunov spectrum of multidimensional continued fraction algorithms

Alien Herrera Torres

Keywords: Lyapunov spectrum | Multidimensional continued fraction algorithms

We prove that the Lyapunov spectrum of the Selmer Multidimensional Continued Fractions Algorithm is simple. The proof is based on the simplicity criterium used by Avila and Viana for proving the Zorich-Kontsevich conjecture. But our approach for checking the pinching and twisting conditions of the criterium is dierent, with a flavor from algebraic geometry. We expect this approach to apply in great generality for continued fraction algorithms.

Anexos:

• These(13Julio).pdf