Weak abelian periodicity of infinite words

We say that an infinite word w is weak abelian periodic if it can be factorized into finite words with the same frequencies of letters. In the paper we study properties of weak abelian periodicity, its relations with balance and frequency. We establish necessary and sufficient conditions for weak abelian periodicity of fixed points of uniform binary morphisms. Also, we discuss weak abelian periodicity in minimal subshifts.