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Dynamical Systems And Linear Algebra at Meripustak

Dynamical Systems And Linear Algebra

Books from same Author: Colonius Fritz

Books from same Publisher: Orient Blackswan Pvt Ltd

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    • General Information  
    Author(s)Colonius Fritz
    PublisherOrient Blackswan Pvt Ltd
    ISBN9781470437299
    Pages304
    BindingPaperback
    LanguageEnglish
    Publish YearJune 2017

    Description

    Orient Blackswan Pvt Ltd Dynamical Systems And Linear Algebra by Colonius Fritz

    This book provides an introduction to the interplay between linear algebra and dynamical systems in continuous time and in discrete time. It first reviews the d autonomous case for one matrix A via induced dynamical systems in R and on Grassmannian manifolds. Then the main no autonomous 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 Eigen spaces 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.