  The aim of the paper is to recover some results of
Cardaliaguet-Nolen-Souganidis in \cite{CNS} and Xin-Yu in \cite{XY} about the
homogenization of the G--equation, using different and simpler techniques. The
main mathematical issue is the lack of coercivity of the Hamiltonians. In our
approach we consider a multivalued dynamics without periodic invariants sets, a
family of intrinsic distances and perform an approximation by a sequence of
coercive Hamiltonians.
