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

次可加性热力学理论是一种主要为研究非共形体系的维度理论而发展起来的工具。近年来，关于自仿射集和自仿射测度的研究取得了很大进展。该项目的目的将是尝试将这些技术用于更一般的非共形系统。最初的研究对象是Rauzy垫片，它与自仿射系统密切相关，但不是严格意义上的自仿射系统。其目的将是研究劳兹垫片的次加热力学形式。

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.