(DOWNLOAD) "An Introduction to Nonautonomous Dynamical Systems and their Attractors" by Peter E. Kloeden & Meihua Yang # Book PDF Kindle ePub Free
eBook details
- Title: An Introduction to Nonautonomous Dynamical Systems and their Attractors
- Author : Peter E. Kloeden & Meihua Yang
- Release Date : January 25, 2020
- Genre: Mathematics,Books,Science & Nature,
- Pages : * pages
- Size : 18461 KB
Description
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.Contents: Dynamical Systems:Autonomous Dynamical SystemsNonautonomous Dynamical Systems: ProcessesSkew Product FlowsEntire Solutions and Invariant SetsPullback Attractors:AttractorsNonautonomous Equilibrium SolutionsAttractors for ProcessesExamples of Pullback Attractors for ProcessesAttractors of Skew Product FlowsForward Attractors and Attracting Sets:Limitations of Pullback Attractors of ProcessesForward AttractorsOmega-Limit Sets and Forward Attracting SetsRandom aAttractors:Random Dynamical SystemsMean-Square Random Dynamical Systems
Readership: Upper level undergraduate, graduate students, researchers in Mathematics and in areas of applications such as biomathematics, ecology, meteorology, medicine, etc.Nonautonomous Ordinary Differential Equations;Autonomous Dynamical Systems;Nonautonomous Dynamical Systems;2-Parameter Semigroups;Skew Product Flows;Strictly Contractive Processes;Pullback Attractors;Forward Attractors;Construction of Pullback and Forward Attractors;Asymptotic Invariance;Nonautonomous Omega-Limit Sets;Forward Attracting Sets;Upper Semi Continuous Dependence on Parameters;Random Dynamical Systems;Random Attractors;Mean-square Random Attractors0Key Features:In recent decades new concepts of nonautonomous attractors have been developed in the mathematical literature and provide a better understanding of the dynamics in nonautonomous systemsThis book aims to make these new ideas accessible to modelers in other areas such as biomathematics, ecology, meteorology, physics, etc.
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