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020 _a9783030509873
_9978-3-030-50987-3
024 7 _a10.1007/978-3-030-50987-3
_2doi
050 4 _aQA267.7
072 7 _aUYA
_2bicssc
072 7 _aCOM014000
_2bisacsh
072 7 _aUYA
_2thema
082 0 4 _a511.352
_223
100 1 _aKuznetsov, Nikolay.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 0 _aAttractor Dimension Estimates for Dynamical Systems: Theory and Computation
_h[electronic resource] :
_bDedicated to Gennady Leonov /
_cby Nikolay Kuznetsov, Volker Reitmann.
250 _a1st ed. 2021.
264 1 _aCham :
_bSpringer International Publishing :
_bImprint: Springer,
_c2021.
300 _aXIX, 545 p. 34 illus., 10 illus. in color.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aEmergence, Complexity and Computation,
_x2194-7295 ;
_v38
505 0 _aAttractors and Lyapunov Functions -- Singular Values, Exterior Calculus and Logarithmic Norms -- Introduction to Dimension Theory. .
520 _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.
650 0 _aComputational complexity.
650 0 _aNonlinear Optics.
650 0 _aSystem theory.
650 1 4 _aComputational Complexity.
650 2 4 _aNonlinear Optics.
650 2 4 _aComplex Systems.
700 1 _aReitmann, Volker.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
710 2 _aSpringerLink (Online service)
773 0 _tSpringer Nature eBook
776 0 8 _iPrinted edition:
_z9783030509866
776 0 8 _iPrinted edition:
_z9783030509880
776 0 8 _iPrinted edition:
_z9783030509897
830 0 _aEmergence, Complexity and Computation,
_x2194-7295 ;
_v38
856 4 0 _uhttps://doi.org/10.1007/978-3-030-50987-3
912 _aZDB-2-ENG
912 _aZDB-2-SXE
942 _cSPRINGER
999 _c185192
_d185192