A NEW VARIATION OF BOWEN%26apos;S FORMULA FOR GRAPH DIRECTED MARKOV SYSTEMS

作者：Roy Mario^*

来源：Discrete and Continuous Dynamical Systems, 2012, 32(7): 2533-2551.

DOI：10.3934/dcds.2012.32.2533

• Iterated function systems
• graph directed Markov systems
• thermodynamic formalism
• Bowen%26apos
• s formula
• pressure
• Hausdorff dimension

We introduce a new variation of Bowen%26apos;s formula for conformal graph directed Markov systems (a.k.a. CGDMSs). This new variation applies to a very large collection of non-irreducible systems and is shown to coincide with the well-known Bowen%26apos;s formula that holds for all finite or finitely irreducible CGDMSs (cf. [2], [4] and [1]). We further show that the original version of Bowen%26apos;s formula may not hold even for non-irreducible CGDMSs whose components are IFSs, justifying thereby the introduction of a new variation. This answers two questions that were raised by Ghenciu and Mauldin in [1]. Their third question is also addressed. Indeed, we prove that Ghenciu and Mauldin%26apos;s conjecture about the finiteness parameters of the partition functions of the pressure is false even within the class of irreducible systems.

• 出版日期2012-7