Geometric Multivalence of Ergodicity, and Entropy within the Topological Thermodynamics: at the Frontier of Order & Chaos

Here the concept of ergodicity is studied, starting from a propaedeutic introduction (Maxwell and Boltzmann), and proving the ergodic Theorems of Birkhoff and Anosov, and the Hopfian statistical process about the ergodicity of the geodesic flow. Then follows a Section aimed at deepening the notion of entropy in relation to the theory of topological thermodynamics, with various related theorems. Excerpt № 7 from my Notes, with ad hoc modifications: removal of all internal cross-references, absence of the Glossary, omission of the recommended readings and of the external references in the background