Title | Linear Chaos |
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Author/s | Karl G. Grosse-Erdmann,Alfred Peris Manguillot |

Year | 2011 |

Publisher | Springer |

ISBN | 978-1-4471-2169-5 (Print) 978-1-4471-2170-1 (Online) |

Link |

It seems fair to say that while research in linear dynamics is still expanding in both depth and breadth, the foundations have reached a certain stage of maturity. At the same time the basic ideas as well as the applications of the field have a broad appeal also to nonspecialists. It is therefore our aim to make the theory of hypercyclic operators and linear chaos accessible to a wider audience. The book is aimed at advanced undergraduate or beginning graduate students, both as a basis for a lecture course and for self-study. We have strived at a self-contained exposition. Each chapter contains a large number of exercises and ends with a section that gives references and directs the reader to further literature. We have tried to keep the necessary prerequisites for reading this book to a minimum. Since the concept of a hypercyclic operator requires both a topological and a linear structure, the reader is supposed to be familiar with

metric spaces (up to the Baire category theorem) and with the basic theory of

Hilbert and Banach spaces, as it is often presented in advanced undergraduate courses on analysis. Moreover, since many examples in the theory are given by operators on spaces of holomorphic functions the reader is also expected to have had an introductory course on complex analysis. Additional, more advanced tools that are only needed occasionally will be provided in the two appendices.

The book is divided into two parts. Part I presents an introduction to the

dynamics of linear operators. Its chapters form a unity and are best studied in that order. In contrast, Part II covers selected topics from linear dynamics. Its chapters are largely independent so that they can be read in an arbitrary order. An occasional cross reference should pose no problem.