Nuevo Libro: Linear Chaos
July 17, 2012 )
Autor/es: Karl G. Grosse-Erdmann
Alfred Peris Manguillot
Descripción: 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
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.