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Attractors under discretisation

Author: Xiaoying Han, (Mathematician); Peter E Kloeden
Publisher: Cham : Springer, 2017.
Series: SpringerBriefs in mathematics.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
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  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version :
Attractors under discretisation.
(OCoLC)988276717
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Xiaoying Han, (Mathematician); Peter E Kloeden
ISBN: 9783319619347 3319619349
OCLC Number: 1021254615
Description: 1 online resource (XI, 122 pages)
Contents: 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.
Series Title: SpringerBriefs in mathematics.
Responsibility: Xiaoying Han, Peter Kloeden.

Abstract:

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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