Linear Chaos

• Main Authors: Grosse-Erdmann, Karl-G (Author), Peris Manguillot, Alfred (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: London : Springer London, 2011.
• Series: Universitext,
• Subjects: Mathematics.; Dynamics.; Ergodic theory.; Functional analysis.; Operator theory.; Dynamical Systems and Ergodic Theory.; Functional Analysis.; Operator Theory.

It is commonly believed that chaos is linked to non-linearity, however many (even quite natural) linear dynamical systems exhibit chaotic behavior. The study of these systems is a young and remarkably active field of research, which has seen many landmark results over the past two decades. Linear dy...

Table of Contents:

• Topological dynamics
• Hypercyclic and chaotic operators
• The Hypercyclicity Criterion
• Classes of hypercyclic and chaotic operators
• Necessary conditions for hypercyclicity and chaos
• Connectedness arguments in linear dynamics
• Dynamics of semigroups, with applications to differential equations
• Existence of hypercyclic operators
• Frequently hypercyclic operators
• Hypercyclic subspaces
• Common hypercyclic vectors
• Linear dynamics in topological vector spaces.