Homoclinic groups, expansive algebraic actions, and actions of sofic groups
Chung, Phu Nhan
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This dissertation has three Chapters. In the first Chapter, we will introduce the main results of the dissertation and review some important definitions. In 1999, Douglas Lind and Klaus Schmidt established the relations between homoclinic groups and entropy properties of an expansive algebraic action of [special characters omitted]. In Chapter 2, we extend their results to expansive algebraic actions of polycyclic-by-finite groups. This chapter is based on the paper , which is joint work with Hanfeng Li. In Chapter 3, we introduce topological pressure for continuous actions of countable sofic groups on compact metrizable spaces. This generalizes the classical topological pressure for continuous actions of countable amenable groups on such spaces. We also establish the variational principle for topological pressure in this sofic context. This chapter is based on my paper .