Abstract
We introduce a new variation of Bowen's formula for conformal graph directedMarkov systems (a.k.a. CGDMSs). This new variation applies to a very largecollection of non-irreducible systems andis shown to coincide with the well-known Bowen's formulathat holds for all finite or finitely irreducibleCGDMSs (cf. [2], [4] and [1]).We further show that the original version of Bowen's formulamay not hold even fornon-irreducible CGDMSs whose components are IFSs,justifying thereby the introduction of a new variation.This answers two questions that were raised by Ghenciu andMauldin in [1]. Their third question is also%partially tackled.addressed. Indeed, we prove that Ghenciu and Mauldin's conjecture about the finitenessparameters of the partition functions of the pressure is false even within the class ofirreducible systems.
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