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Geometric Theory of Discrete Nonautonomous Dynamical Systems

2010-09-17 Mathematics
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Release : 2010-09-17
Genre : Mathematics
Kind : eBook
Book Rating : 575/5 ( reviews)

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Book Synopsis Geometric Theory of Discrete Nonautonomous Dynamical Systems by : Christian Pötzsche

Download or read book Geometric Theory of Discrete Nonautonomous Dynamical Systems written by Christian Pötzsche. This book was released on 2010-09-17. Available in PDF, EPUB and Kindle. Book excerpt: The goal of this book is to provide an approach to the corresponding geometric theory of nonautonomous discrete dynamical systems in infinite-dimensional spaces by virtue of 2-parameter semigroups (processes).

Dynamical Systems

2010-08-03 Mathematics
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Release : 2010-08-03
Genre : Mathematics
Kind : eBook
Book Rating : 229/5 ( reviews)

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Book Synopsis Dynamical Systems by : Werner Krabs

Download or read book Dynamical Systems written by Werner Krabs. This book was released on 2010-08-03. Available in PDF, EPUB and Kindle. Book excerpt: At the end of the nineteenth century Lyapunov and Poincaré developed the so called qualitative theory of differential equations and introduced geometric- topological considerations which have led to the concept of dynamical systems. In its present abstract form this concept goes back to G.D. Birkhoff. This is also the starting point of Chapter 1 of this book in which uncontrolled and controlled time-continuous and time-discrete systems are investigated. Controlled dynamical systems could be considered as dynamical systems in the strong sense, if the controls were incorporated into the state space. We, however, adapt the conventional treatment of controlled systems as in control theory. We are mainly interested in the question of controllability of dynamical systems into equilibrium states. In the non-autonomous time-discrete case we also consider the problem of stabilization. We conclude with chaotic behavior of autonomous time discrete systems and actual real-world applications.

An Introduction To Nonautonomous Dynamical Systems And Their Attractors

2020-11-25 Mathematics
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Release : 2020-11-25
Genre : Mathematics
Kind : eBook
Book Rating : 671/5 ( reviews)

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Book Synopsis An Introduction To Nonautonomous Dynamical Systems And Their Attractors by : Peter Kloeden

Download or read book An Introduction To Nonautonomous Dynamical Systems And Their Attractors written by Peter Kloeden. This book was released on 2020-11-25. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Attractors for infinite-dimensional non-autonomous dynamical systems

2012-09-26 Mathematics
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Release : 2012-09-26
Genre : Mathematics
Kind : eBook
Book Rating : 809/5 ( reviews)

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Book Synopsis Attractors for infinite-dimensional non-autonomous dynamical systems by : Alexandre Carvalho

Download or read book Attractors for infinite-dimensional non-autonomous dynamical systems written by Alexandre Carvalho. This book was released on 2012-09-26. Available in PDF, EPUB and Kindle. Book excerpt: The book treats the theory of attractors for non-autonomous dynamical systems. The aim of the book is to give a coherent account of the current state of the theory, using the framework of processes to impose the minimum of restrictions on the nature of the non-autonomous dependence. The book is intended as an up-to-date summary of the field, but much of it will be accessible to beginning graduate students. Clear indications will be given as to which material is fundamental and which is more advanced, so that those new to the area can quickly obtain an overview, while those already involved can pursue the topics we cover more deeply.

Difference Equations, Discrete Dynamical Systems and Applications

2015-12-01 Mathematics
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Release : 2015-12-01
Genre : Mathematics
Kind : eBook
Book Rating : 476/5 ( reviews)

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Book Synopsis Difference Equations, Discrete Dynamical Systems and Applications by : Martin Bohner

Download or read book Difference Equations, Discrete Dynamical Systems and Applications written by Martin Bohner. This book was released on 2015-12-01. Available in PDF, EPUB and Kindle. Book excerpt: These proceedings of the 20th International Conference on Difference Equations and Applications cover the areas of difference equations, discrete dynamical systems, fractal geometry, difference equations and biomedical models, and discrete models in the natural sciences, social sciences and engineering. The conference was held at the Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences (Hubei, China), under the auspices of the International Society of Difference Equations (ISDE) in July 2014. Its purpose was to bring together renowned researchers working actively in the respective fields, to discuss the latest developments, and to promote international cooperation on the theory and applications of difference equations. This book will appeal to researchers and scientists working in the fields of difference equations, discrete dynamical systems and their applications.

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