03148nam 22006015 450 991048365060332120251113182055.03-030-50987-710.1007/978-3-030-50987-3(CKB)4100000011325531(DE-He213)978-3-030-50987-3(MiAaPQ)EBC6271218(PPN)258866004(MiAaPQ)EBC29095601(EXLCZ)99410000001132553120200702d2021 u| 0engurnn#---mamaatxtrdacontentcrdamediacrrdacarrierAttractor Dimension Estimates for Dynamical Systems: Theory and Computation Dedicated to Gennady Leonov /by Nikolay Kuznetsov, Volker Reitmann1st ed. 2021.Cham :Springer International Publishing :Imprint: Springer,2021.1 online resource (XIX, 545 pages) : 34 illus., 10 illus. in color.)Emergence, Complexity and Computation,2194-7295 ;38Includes index.3-030-50986-9 Attractors and Lyapunov Functions -- Singular Values, Exterior Calculus and Logarithmic Norms -- Introduction to Dimension Theory. .This book provides analytical and numerical methods for the estimation of dimension characteristics (Hausdorff, Fractal, Carathéodory dimensions) for attractors and invariant sets of dynamical systems and cocycles generated by smooth differential equations or maps in finite-dimensional Euclidean spaces or on manifolds. It also discusses stability investigations using estimates based on Lyapunov functions and adapted metrics. Moreover, it introduces various types of Lyapunov dimensions of dynamical systems with respect to an invariant set, based on local, global and uniform Lyapunov exponents, and derives analytical formulas for the Lyapunov dimension of the attractors of the Hénon and Lorenz systems. Lastly, the book presents estimates of the topological entropy for general dynamical systems in metric spaces and estimates of the topological dimension for orbit closures of almost periodic solutions to differential equations.Emergence, Complexity and Computation,2194-7295 ;38Computational complexityNonlinear OpticsSystem theoryComputational ComplexityNonlinear OpticsComplex SystemsComputational complexity.Nonlinear Optics.System theory.Computational Complexity.Nonlinear Optics.Complex Systems.515.39Kuznetsov N. V(Nikolay Vladimirovich),authttp://id.loc.gov/vocabulary/relators/aut1275689Reitmann Volker1948-authttp://id.loc.gov/vocabulary/relators/autMiAaPQMiAaPQMiAaPQBOOK9910483650603321Attractor Dimension Estimates for Dynamical Systems: Theory and Computation4464463UNINA