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An introduction to nonautonomous dynamical systems and their attractors /

Record Type:	Language materials, printed : Monograph/item
Title/Author:	An introduction to nonautonomous dynamical systems and their attractors /Peter E Kloeden, Meihua Yang.
Author:	Kloeden, Peter E.,
other author:	Yang, Meihua
Description:	xii, 144 pages :illustrations ;26 cm.
Subject:	Dynamics.
ISBN:	9789811228650

An introduction to nonautonomous dynamical systems and their attractors /
Kloeden, Peter E.,

An introduction to nonautonomous dynamical systems and their attractors /Peter E Kloeden, Meihua Yang. - xii, 144 pages :illustrations ;26 cm. - Interdisciplinary mathematical sciences,vol. 211793-1355 ;. - Interdisciplinary mathematical sciences ;v. 9..

Includes bibliographical references and index.

Autonomous dynamical systems -- Nonautonomous dynamical systems: processes -- Skew product flows -- Entire solutions and invariant sets -- Attractors -- Nonautonomous equilibrium solutions -- Attractors for processes -- Examples of pullback attractors for processes -- Attractors of skew product flows -- Limitations of pullback attractors of processes -- Forward attractors -- Omega-limit sets and forward attracting sets -- Random dynamical systems -- Mean-square random dynamical systems.

"The nature of time in a nonautonomous dynamical system is very different from that in autonomous systems, which depend only on the time that has elapsed since starting rather than on the actual time itself. Consequently, limiting objects may not exist in actual time as in autonomous systems. New concepts of attractors in nonautonomous dynamical system are thus required. In addition, the definition of a dynamical system itself needs to be generalised to the nonautonomous context. Here two possibilities are considered: two-parameter semigroups or processes and the skew product flows. Their attractors are defined in terms of families of sets that are mapped onto each other under the dynamics rather than a single set as in autonomous systems. Two types of attraction are now possible: pullback attraction, which depends on the behaviour from the system in the distant past, and forward attraction, which depends on the behaviour of the system in the distant future. These are generally independent of each other. The component subsets of pullback and forward attractors exist in actual time. The asymptotic behaviour in the future limit is characterised by omega-limit sets, in terms of which form what are called forward attracting sets. They are generally not invariant in the conventional sense, but are asymptotically invariant in general and, if the future dynamics is appropriately uniform, also asymptotically negatively invariant. Much of this book is based on lectures given by the authors in Frankfurt and Wuhan. It was written mainly when the first author held a "Thousand Expert" Professorship at the Huazhong University of Science and Technology in Wuhan"--

ISBN: 9789811228650

LCCN: 2020051829Subjects--Topical Terms:

189568
Dynamics.

LC Class. No.: QA845 / .K55 2021

Dewey Class. No.: 515/.39

An introduction to nonautonomous dynamical systems and their attractors /
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100 1 $a Kloeden, Peter E., $e author. $3 916233
245 1 3 $a An introduction to nonautonomous dynamical systems and their attractors / $c Peter E Kloeden, Meihua Yang.
264 1 $a New Jersey : $b World Scientific, $c [2021]
300 $a xii, 144 pages : $b illustrations ; $c 26 cm.
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490 1 $a Interdisciplinary mathematical sciences, $x 1793-1355 ; $v vol. 21
504 $a Includes bibliographical references and index.
505 0 $a Autonomous dynamical systems -- Nonautonomous dynamical systems: processes -- Skew product flows -- Entire solutions and invariant sets -- Attractors -- Nonautonomous equilibrium solutions -- Attractors for processes -- Examples of pullback attractors for processes -- Attractors of skew product flows -- Limitations of pullback attractors of processes -- Forward attractors -- Omega-limit sets and forward attracting sets -- Random dynamical systems -- Mean-square random dynamical systems.
520 $a "The nature of time in a nonautonomous dynamical system is very different from that in autonomous systems, which depend only on the time that has elapsed since starting rather than on the actual time itself. Consequently, limiting objects may not exist in actual time as in autonomous systems. New concepts of attractors in nonautonomous dynamical system are thus required. In addition, the definition of a dynamical system itself needs to be generalised to the nonautonomous context. Here two possibilities are considered: two-parameter semigroups or processes and the skew product flows. Their attractors are defined in terms of families of sets that are mapped onto each other under the dynamics rather than a single set as in autonomous systems. Two types of attraction are now possible: pullback attraction, which depends on the behaviour from the system in the distant past, and forward attraction, which depends on the behaviour of the system in the distant future. These are generally independent of each other. The component subsets of pullback and forward attractors exist in actual time. The asymptotic behaviour in the future limit is characterised by omega-limit sets, in terms of which form what are called forward attracting sets. They are generally not invariant in the conventional sense, but are asymptotically invariant in general and, if the future dynamics is appropriately uniform, also asymptotically negatively invariant. Much of this book is based on lectures given by the authors in Frankfurt and Wuhan. It was written mainly when the first author held a "Thousand Expert" Professorship at the Huazhong University of Science and Technology in Wuhan"-- $c Provided by publisher.
650 0 $a Dynamics. $3 189568
650 0 $a Attractors (Mathematics) $3 239620
650 0 $a Random dynamical systems. $3 265309
650 6 $a Dynamique. $3 283557
650 6 $a Attracteurs (Mathématiques) $3 916326
650 6 $a Systémes dynamiques aléatoires. $3 916327
700 1 $a Yang, Meihua $c (Professor of Mathematics), $e author. $3 916234
830 0 $a Interdisciplinary mathematical sciences ; $v v. 9. $3 575246
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