  The effectivity up to R-linear equivalence (Dirichlet property) of
pseudoeffective adelic R-Cartier divisors is a subtle problem in arithmetic
geometry. In this article, we propose sufficient conditions for the Dirichlet
property by using the dynamic system in the classic Arakelov geometry setting.
We also give a numerical criterion of the Dirichlet property for adelic
R-Cartier divisors on curves over a trivially valued field.
