000 03568nam a22005055i 4500
001 978-1-4471-2170-1
003 DE-He213
005 20140220083731.0
007 cr nn 008mamaa
008 110822s2011 xxk| s |||| 0|eng d
020 _a9781447121701
_9978-1-4471-2170-1
024 7 _a10.1007/978-1-4471-2170-1
_2doi
050 4 _aQA313
072 7 _aPBWR
_2bicssc
072 7 _aMAT034000
_2bisacsh
082 0 4 _a515.39
_223
082 0 4 _a515.48
_223
100 1 _aGrosse-Erdmann, Karl-G.
_eauthor.
245 1 0 _aLinear Chaos
_h[electronic resource] /
_cby Karl-G. Grosse-Erdmann, Alfred Peris Manguillot.
264 1 _aLondon :
_bSpringer London,
_c2011.
300 _aXII, 388p. 28 illus.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aUniversitext,
_x0172-5939
505 0 _aTopological 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.
520 _aIt 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.
650 0 _aMathematics.
650 0 _aDifferentiable dynamical systems.
650 0 _aFunctional analysis.
650 0 _aOperator theory.
650 1 4 _aMathematics.
650 2 4 _aDynamical Systems and Ergodic Theory.
650 2 4 _aFunctional Analysis.
650 2 4 _aOperator Theory.
700 1 _aPeris Manguillot, Alfred.
_eauthor.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9781447121695
830 0 _aUniversitext,
_x0172-5939
856 4 0 _uhttp://dx.doi.org/10.1007/978-1-4471-2170-1
912 _aZDB-2-SMA
999 _c106174
_d106174