  The two-dimensional homogeneous Euclidean algorithm is the central motivation
for the definition of the classical multidimensional continued fraction
algorithms, as Jacobi-Perron, Poincar\'e, 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.

Dynamical Systems