Chaos and entropy in linear dynamical system

Abstract: We discuss various notions of chaos in the context of linear dynamics. Many types of chaos (for linear operators) can only occur within infinite dimensional vector spaces. Two specific categories of these spaces on which we focus are weighted sequence spaces and function spaces, and the natural operators on these spaces are backward shifts and translations (respectively). We discuss relationships between the types of chaos for these operators and characterizations for them in terms of the weight sequence/function. More generally, we examine how chaos and entropy relate to the eigenvalues of the operator. Throughout, we highlight recent and current projects completed with undergraduate students.

dynamical systems

Audience: researchers in the topic

Little school dynamics

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