Developing connections between dimension and the sub-additive thermodynamic formalism.

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The sub-additive thermodynamic formalism is a tool which has been developed mainly for the study of the dimension theory for non-conformal systems. Recently there has been a lot of development in this area for self-affine sets and measures. The aim of this project will be to try to use and develop these techniques for more general non- conformal systems. The initial object of study will be the Rauzy gasket which is closely related to self-affine systems but is not strictly self-affine. The aim will be to study the subadditive thermodynamic formalism for the Rauzy gasket.