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Attractors under discretisation

Han, Xiaoying.

Attractors under discretisation

Record Type:	Electronic resources : Monograph/item
Title/Author:	Attractors under discretisationby Xiaoying Han, Peter Kloeden.
Author:	Han, Xiaoying.
other author:	Kloeden, Peter.
Published:	Cham :Springer International Publishing :2017.
Description:	xi, 122 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
Subject:	Attractors (Mathematics)
Online resource:	http://dx.doi.org/10.1007/978-3-319-61934-7
ISBN:	9783319619347$q(electronic bk.)

Attractors under discretisation
Han, Xiaoying.

Attractors under discretisation[electronic resource] /by Xiaoying Han, Peter Kloeden. - Cham :Springer International Publishing :2017. - xi, 122 p. :ill., digital ;24 cm. - SpringerBriefs in mathematics,2191-8198. - SpringerBriefs in mathematics..

Part I Dynamical systems and numerical schemes -- 1 Lyapunov stability and dynamical systems -- 2 One step numerical schemes -- Part II Steady states under discretization -- 3 Linear systems -- 4 Lyapunov functions -- 5 Dissipative systems with steady states -- 6 Saddle points under discretisation. Part III Autonomous attractors under discretization -- 7 Dissipative systems with attractors -- 8 Lyapunov functions for attractors -- 9 Discretisation of an attractor. Part IV Nonautonomous limit sets under discretization -- 10 Dissipative nonautonomous systems -- 11 Discretisation of nonautonomous limit sets -- 12 Variable step size -- 13 Discretisation of a uniform pullback attractor -- Notes -- References.

This work focuses on the preservation of attractors and saddle points of ordinary differential equations under discretisation. In the 1980s, key results for autonomous ordinary differential equations were obtained - by Beyn for saddle points and by Kloeden & Lorenz for attractors. One-step numerical schemes with a constant step size were considered, so the resulting discrete time dynamical system was also autonomous. One of the aims of this book is to present new findings on the discretisation of dissipative nonautonomous dynamical systems that have been obtained in recent years, and in particular to examine the properties of nonautonomous omega limit sets and their approximations by numerical schemes - results that are also of importance for autonomous systems approximated by a numerical scheme with variable time steps, thus by a discrete time nonautonomous dynamical system.

ISBN: 9783319619347$q(electronic bk.)

Standard No.: 10.1007/978-3-319-61934-7doiSubjects--Topical Terms:

239620
Attractors (Mathematics)

LC Class. No.: QA614.813 / .H36 2017

Dewey Class. No.: 515.39

Attractors under discretisation
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505 0 $a Part I Dynamical systems and numerical schemes -- 1 Lyapunov stability and dynamical systems -- 2 One step numerical schemes -- Part II Steady states under discretization -- 3 Linear systems -- 4 Lyapunov functions -- 5 Dissipative systems with steady states -- 6 Saddle points under discretisation. Part III Autonomous attractors under discretization -- 7 Dissipative systems with attractors -- 8 Lyapunov functions for attractors -- 9 Discretisation of an attractor. Part IV Nonautonomous limit sets under discretization -- 10 Dissipative nonautonomous systems -- 11 Discretisation of nonautonomous limit sets -- 12 Variable step size -- 13 Discretisation of a uniform pullback attractor -- Notes -- References.
520 $a This work focuses on the preservation of attractors and saddle points of ordinary differential equations under discretisation. In the 1980s, key results for autonomous ordinary differential equations were obtained - by Beyn for saddle points and by Kloeden & Lorenz for attractors. One-step numerical schemes with a constant step size were considered, so the resulting discrete time dynamical system was also autonomous. One of the aims of this book is to present new findings on the discretisation of dissipative nonautonomous dynamical systems that have been obtained in recent years, and in particular to examine the properties of nonautonomous omega limit sets and their approximations by numerical schemes - results that are also of importance for autonomous systems approximated by a numerical scheme with variable time steps, thus by a discrete time nonautonomous dynamical system.
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