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Catalogue Information
Field name	Details
Dewey Class	515.39
Dewey Class	515.48
Title	Linear Chaos ([Ebook]) / by Karl-G. Grosse-Erdmann, Alfred Peris Manguillot.
Author	Grosse-Erdmann, Karl-Goswin
Added Personal Name	Peris Manguillot, Alfred
Other name(s)	SpringerLink (Online service)
Publication	London : Springer London , 2011
Physical Details	XII, 388 pages:. 28 illus. : online resource.
Series	Universitext 0172-5939
ISBN	9781447121701
Summary Note	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 dynamics lies at the crossroads of several areas of mathematics including operator theory, complex analysis, ergodic theory and partial differential equations. At the same time its basic ideas can be easily understood by a wide audience. Written by two renowned specialists, Linear Chaos provides a welcome introduction to this theory. Split into two parts, part I presents a self-contained introduction to the dynamics of linear operators, while part II covers selected, largely independent topics from linear dynamics.Â More than 350 exercises and many illustrations are included, and each chapter contains a further âSources and Commentsâ section. The only prerequisites are a familiarity with metric spaces, the basic theory of Hilbert and Banach spaces and fundamentals of complex analysis. More advanced tools, only needed occasionally, are provided in two appendices. A self-contained exposition, this book will be suitable for self-study and will appeal to advanced undergraduate or beginning graduate students. It will also be of use to researchers in other areas of mathematics such as partial differential equations, dynamical systems and ergodic theory.:
Contents note	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.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users).
Internet Site	http://dx.doi.org/10.1007/978-1-4471-2170-1
Links to Related Works	Subject References: Differentiable dynamical systems . Dynamical systems and ergodic theory . Functional Analysis . Mathematics . Operator Theory . Authors: author . Grosse-Erdmann, Karl-Goswin . Peris Manguillot, Alfred . Corporate Authors: SpringerLink (Online service) . Series: Universitext . Classification: 515.39 . 515.48 . 515.39 (DDC 23) .

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Linear Chaos

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