00000cmm a22000004a 4500 UP-99796217611212394 Buklod 20241113140903.0 m go j cr cn |||aaaaa 241113s2011 xxk||||go||j| ||||||engdd 9781447121701 (eBook) 1447121708 (eBook) 9781447121695 (iLib)UPD-00215704156 CSt DMLR rda eng DMLUC Q 172.5 C45 G76 2011eb Grosse-Erdmann, Karl-Goswin author Linear chaos Karl-G. Grosse-Erdmann, Alfred Peris Manguillot. London New York Springer c2011 1 online resource (xi, 386 pages) text rdacontent computer rdamedia online resource rdacarrier Universitext 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 IP-based subscription, access limited to within on-campus computer network Access via Electronic Resources of the UPD University Library Website 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.  More than 350 exercises and many illustrations are included, and each chapter contains a further ?Sources and Comments? 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 --Provided by publisher Electronic reproduction New York SpringerLink 2011 Available via World Wide Web through SpringerLink Chaotic behavior in systems. Linear operators. Manguillot, Alfred Peris author. SpringerLink (Online service). http://link.springer.com/book/10.1007/978-1-4471-2170-1 Available for University of the Philippines Diliman via SpringerLink. Click here to access FO UPD DMLR Q 172.5 C45 G76 2011eb Electronic Resource