  The classical Gauss Map is a piecewise continuous map from the unit interval
to itself. From this map we retrieve the continued fraction expansion of
irrational numbers and its dynamical properties give information about some
arithmetic and algebraic properties of irrational numbers. In this notes we
will explore some generalizations of the Gauss Map to higher dimensions and
pose some questions and conjectures about the arithmetic/algebraic information
that these maps may carry.
