國立虎尾科技大學 |

Attractor Dimension Estimates for Dynamical Systems: Theory and Computation = Dedicated to Gennady Leonov /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Attractor Dimension Estimates for Dynamical Systems: Theory and Computation/ by Nikolay Kuznetsov, Volker Reitmann.
其他題名:	Dedicated to Gennady Leonov /
作者:	Kuznetsov, Nikolay.
其他作者:	Reitmann, Volker.
面頁冊數:	XIX, 545 p. 34 illus., 10 illus. in color.online resource. :
Contained By:	Springer Nature eBook
標題:	Complex Systems. -
電子資源:	https://doi.org/10.1007/978-3-030-50987-3
ISBN:	9783030509873

Attractor Dimension Estimates for Dynamical Systems: Theory and Computation = Dedicated to Gennady Leonov /
Kuznetsov, Nikolay.

Attractor Dimension Estimates for Dynamical Systems: Theory and ComputationDedicated to Gennady Leonov /[electronic resource] :by Nikolay Kuznetsov, Volker Reitmann. - 1st ed. 2021. - XIX, 545 p. 34 illus., 10 illus. in color.online resource. - Emergence, Complexity and Computation,382194-7295 ;. - Emergence, Complexity and Computation,12.

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.

ISBN: 9783030509873

Standard No.: 10.1007/978-3-030-50987-3doiSubjects--Topical Terms:

888664
Complex Systems.

LC Class. No.: QA75.5-76.95

Dewey Class. No.: 004.0151

Attractor Dimension Estimates for Dynamical Systems: Theory and Computation = Dedicated to Gennady Leonov /
LDR:02601nam a22004335i 4500 001 1048307
003 DE-He213
005 20211118100804.0
007 cr nn 008mamaa
008 220103s2021 sz | s |||| 0|eng d
020 $a 9783030509873 $9 978-3-030-50987-3
024 7 $a 10.1007/978-3-030-50987-3 $2 doi
035 $a 978-3-030-50987-3
050 4 $a QA75.5-76.95
050 4 $a QA76.63
072 7 $a UY $2 bicssc
072 7 $a COM014000 $2 bisacsh
072 7 $a UY $2 thema
072 7 $a UYA $2 thema
082 0 4 $a 004.0151 $2 23
100 1 $a Kuznetsov, Nikolay. $e author. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 1352138
245 1 0 $a Attractor Dimension Estimates for Dynamical Systems: Theory and Computation $h [electronic resource] : $b Dedicated to Gennady Leonov / $c by Nikolay Kuznetsov, Volker Reitmann.
250 $a 1st ed. 2021.
264 1 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2021.
300 $a XIX, 545 p. 34 illus., 10 illus. in color. $b online resource.
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
347 $a text file $b PDF $2 rda
490 1 $a Emergence, Complexity and Computation, $x 2194-7295 ; $v 38
505 0 $a Attractors and Lyapunov Functions -- Singular Values, Exterior Calculus and Logarithmic Norms -- Introduction to Dimension Theory. .
520 $a 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.
650 2 4 $a Complex Systems. $3 888664
650 2 4 $a Applications of Nonlinear Dynamics and Chaos Theory. $3 1113607
650 1 4 $a Theory of Computation. $3 669322
650 0 $a Dynamical systems. $3 1249739
650 0 $a Statistical physics. $3 528048
650 0 $a Computers. $3 565115
700 1 $a Reitmann, Volker. $e author. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 1352139
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer Nature eBook
776 0 8 $i Printed edition: $z 9783030509866
776 0 8 $i Printed edition: $z 9783030509880
776 0 8 $i Printed edition: $z 9783030509897
830 0 $a Emergence, Complexity and Computation, $x 2194-7287 ; $v 12 $3 1254548
856 4 0 $u https://doi.org/10.1007/978-3-030-50987-3
912 $a ZDB-2-ENG
912 $a ZDB-2-SXE
950 $a Engineering (SpringerNature-11647)
950 $a Engineering (R0) (SpringerNature-43712)