000			nam a22 4500
999			_c32678 _d32678
008			240213b xxu||||| |||| 00| 0 eng d
020			_a9781470437299
082			_a512.5 _bCOL
100			_aColonius, Fritz
245			_aDynamical systems and linear algebra
260			_bAmerican Mathematical Society, _c2014 _aProvidence :
300			_axv, 284 p. : _bill., _c24 cm.
365			_b1405.00 _c₹ _d01
490			_aGraduate studies in mathematics ; _vv.158
504			_aIncludes bibliographical references and index.
520			_aThis book provides n introduction to the interplay between linear algebra and dynamical systems in continuous time and in discrete time. It first reviews the autonomous case for one matrix A via induced dynamical systems in ℝᵈ and on Grassmannian manifolds. Then the main nonautonomous approaches are presented for which the time dependency of A(t) is given via skew-product flows using periodicity, or topological (chain recurrence) or ergodic properties (invariant measures). The authors develop generalizations of (real parts of) eigenvalues and eigenspaces as a starting point for a linear algebra for classes of time-varying linear systems, namely periodic, random, and perturbed (or controlled) systems. The book presents for the first time in one volume a unified approach via Lyapunov exponents to detailed proofs of Floquet theory, of the properties of the Morse spectrum, and of the multiplicative ergodic theorem for products of random matrices. The main tools, chain recurrence and Morse decompositions, as well as classical ergodic theory are introduced in a way that makes the entire material accessible for beginning graduate students.
650			_aTopological dynamics
650			_aVector bundle
650			_aAttractor
650			_aChain components
650			_aEigenvalues
650			_aFloquet theory
650			_aAlgebras Linear
650			_aMatrix theory
650			_aJordan block
650			_aLyapunov spaces
650			_aMetric dynamical system
650			_aSubadditive ergodic theorem
650			_aMultiplicative Ergodic Theorem
650			_aPeriodic matrix
650			_aProbability theory
700			_aKliemann, Wolfgang
942			_2ddc _cBK