1.

Record Nr.

UNINA9910254302003321

Autore

Han Xiaoying

Titolo

Attractors under discretisation / / by Xiaoying Han, Peter Kloeden

Pubbl/distr/stampa

Cham : , : Springer International Publishing : , : Imprint : Springer, , 2017

ISBN

3-319-61934-9

Edizione

[1st ed. 2017.]

Descrizione fisica

1 online resource (121 pages)

Collana

SpringerBriefs in Mathematics, , 2191-8198

Disciplina

514.74

Soggetti

Numerical analysis

Dynamics

Ergodic theory

Differential equations

Numerical Analysis

Dynamical Systems and Ergodic Theory

Ordinary Differential Equations

Lingua di pubblicazione

Inglese

Formato

Materiale a stampa

Livello bibliografico

Monografia

Nota di contenuto

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.

Sommario/riassunto

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.