An Overview of IFS with Applications to Thermodynamical Formalism

In this talk, we present an overview of modern Iterated Function System (IFS) theory, highlighting its geometric, topological, and dynamical aspects, along with several recent developments in the field. We then discuss applications to Thermodynamical Formalism, focusing on holonomic measures and results obtained in recent collaborations with R. R. Souza, A. O. Lopes, J. K. Mengue, among others.