Linear chaos

The notes are a companion material to the course Linear Chaos, offered at the University of Innsbruck in the Academic Year 2025/2026, and taught by Christian Bargetz and myself. Most of the course follows closely the textbook Linear Chaos (see the references below) and these notes only cover the topics where our presentation differs from said book. In particular, the notes assume that the reader is familiar with the definitions and results in the first three chapters of this textbook. Moreover, it is assumed that the reader has a certain familiarity with basic Complex Analysis, Functional Analysis, and Topology. In particular, readers should be familiar with the basic properties of holomorphic functions, such as Cauchy’s integral formula, power series expansions, the identity principle, and the classification of isolated singularities. From Functional Analysis, essentially only the Hahn–Banach theorem is used. Finally, readers should have some acquaintance with general topology, in particular connected sets and connected components.