Exactness of the Euclidean algorithm and of the Rauzy induction on the space of interval exchange transformations

Arnaldo Nogueira (1)

1 I2M - Institut de Mathématiques de Marseille

The two-dimensional homogeneous Euclidean algorithm is the central motivation for the definition of the classical multidimensional continued fraction algorithms, such as Jacobi–Perron, Poincaré, Brun and Selmer algorithms. The Rauzy induction, a generalization of the Euclidean algorithm, is a key tool in the study of interval exchange transformations. Both maps are known to be dissipative and ergodic with respect to Lebesgue measure. Here we prove that they are exact.

Domaines: Systèmes dynamiques [math.DS]

Arnaldo Nogueira. Exactness of the Euclidean algorithm and of the Rauzy induction on the space of interval exchange transformations. Ergodic Theory and Dynamical Systems, 2013, 33 (01), pp.221 ­ 246. ⟨10.1017/S014338571100085X⟩. ⟨hal-01268342⟩