Jean-Baptiste Cadart: Linear Chaotic Systems

Abstract

 Most of the time, when we think about chaos, we think about fractals and systems ruled by non-linear differential equations. However, a lot of chaotic systems are in fact linear! There are two characteristics a linear chaotic system should respect: being a hypercycle and having a dense set of periodic points. We will introduce this theory by presenting the Fréchet spaces, the notion of topological transitivity, the Birkhoff theorem, linear dynamical systems and the Kitai Criteria as well as show that the derivative operator is chaotic!