LEADER 03148nam 22006015 450 001 9910483650603321 005 20251113182055.0 010 $a3-030-50987-7 024 7 $a10.1007/978-3-030-50987-3 035 $a(CKB)4100000011325531 035 $a(DE-He213)978-3-030-50987-3 035 $a(MiAaPQ)EBC6271218 035 $a(PPN)258866004 035 $a(MiAaPQ)EBC29095601 035 $a(EXLCZ)994100000011325531 100 $a20200702d2021 u| 0 101 0 $aeng 135 $aurnn#---mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aAttractor Dimension Estimates for Dynamical Systems: Theory and Computation $eDedicated to Gennady Leonov /$fby Nikolay Kuznetsov, Volker Reitmann 205 $a1st ed. 2021. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2021. 215 $a1 online resource (XIX, 545 pages) : 34 illus., 10 illus. in color.) 225 1 $aEmergence, Complexity and Computation,$x2194-7295 ;$v38 300 $aIncludes index. 311 0 $a3-030-50986-9 327 $aAttractors and Lyapunov Functions -- Singular Values, Exterior Calculus and Logarithmic Norms -- Introduction to Dimension Theory. . 330 $aThis book provides analytical and numerical methods for the estimation of dimension characteristics (Hausdorff, Fractal, Carathéodory dimensions) for attractors and invariant sets of dynamical systems and cocycles generated by smooth differential equations or maps in finite-dimensional Euclidean spaces or on manifolds. It also discusses stability investigations using estimates based on Lyapunov functions and adapted metrics. Moreover, it introduces various types of Lyapunov dimensions of dynamical systems with respect to an invariant set, based on local, global and uniform Lyapunov exponents, and derives analytical formulas for the Lyapunov dimension of the attractors of the Hénon and Lorenz systems. Lastly, the book presents estimates of the topological entropy for general dynamical systems in metric spaces and estimates of the topological dimension for orbit closures of almost periodic solutions to differential equations. 410 0$aEmergence, Complexity and Computation,$x2194-7295 ;$v38 606 $aComputational complexity 606 $aNonlinear Optics 606 $aSystem theory 606 $aComputational Complexity 606 $aNonlinear Optics 606 $aComplex Systems 615 0$aComputational complexity. 615 0$aNonlinear Optics. 615 0$aSystem theory. 615 14$aComputational Complexity. 615 24$aNonlinear Optics. 615 24$aComplex Systems. 676 $a515.39 700 $aKuznetsov$b N. V$g(Nikolay Vladimirovich),$4aut$4http://id.loc.gov/vocabulary/relators/aut$01275689 702 $aReitmann$b Volker$f1948-$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910483650603321 996 $aAttractor Dimension Estimates for Dynamical Systems: Theory and Computation$94464463 997 $aUNINA