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Global Attractors of Set-Valued Dynamical and Control Systems
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Authors: David N. Cheban (Department of Mathematics and Informatics, State University of Moldova, Republic of Moldova) 
Book Description:
In this book the results on set-valued dynamical systems (dynamical systems without uniqueness) and some adjoining problems are studied. A part of the book is dedicated to the study of global attractors of control systems (as application of our general results concerning the compact global attractors of general set-valued dynamical systems).
This book is the first to study the global attractors of set-valued dynamical and control systems. The basic results are contained in the courses of lectures which author has given during many years.

Table of Contents:
Preface
1. Notation

Chapter 1. Set-Valued Dynamical Systems and Other Topics pp.1-18
1.1. Set-valued functions and differential inclusions
1.2. Shift dynamical systems
1.3. Set-valued dynamical systems
1.4. Examples of set–valued dynamical systems
1.5. ů–limit sets and prolongation of funnels
1.6. Some properties of multi-dimensional systems

Chapter 2. Set-Valued Dissipative Dynamical Systems pp.19-70
2.1. Limit properties of set–valued dynamical systems
2.2.Center of Levinson of a set–valued dissipative dynamical system
2.3. Dissipative dynamical systems in locally compact metric spaces
2.4. Structure of Levinson center
2.5. Locally dissipative dynamical systems
2.6. Trajectory dissipativity
2.7. Asymptotic stability of compact positively invariant sets
2.8. Connectedness of Levinson center
2.9. b–dissipative set-valued dynamical systems
2.10. Some applications of set-valued dissipative dynamical systems

Chapter 3. Non-Autonomous Dissipative Dynamical Systems pp.71-118
3.1. Set-valued non-autonomous dynamical systems (NDS)
3.2. Stability of Levinson center of NDS
3.3. Dissipative dynamical systems in finite-dimensional spaces
3.4. Non-periodic dissipative differential inclusions
3.5. Lyapunov functions method
3.6. Global attractors of autonomous set-valued dynamical systems
3.7. Global attractors of NDS
3.8. Pull back attractors of set-valued co-cycles
3.9. Global attractors of differential and difference inclusions
3.10.Relation between different types of global attractors of NDS
3.11.Comments and references

Chapter 4. Non-Autonomous Dynamical Systems with Convergence pp.119-144
4.1. Non-autonomous dynamical systems with convergence
4.2. Linear systems
4.3. Asymptotics of solutions of homogeneous dynamical systems
4.4. Asymptotic behavior of multi-dimensionalsystems
4.5. Ordinary differential equations in a Banach space
4.6. Functional differential equations
4.7. Quasi-linear parabolic equations

Chapter 5. Dependence on Parameters pp.145-172
5.1. Maximal compact invariant sets
5.2. Uppersemi-continuity
5.3. Connectedness
5.4. Some applications
5.5. Uppersemi-continuous invariant sections and their continuous dependence on parameters
5.6. Some properties of Lipschitzian mappings
5.7. Continuous dependence of attractors of IFS1

Chapter 6. Compact Global Attractors of Control Systems pp.173-208
6.1. Upper semi-continuous invariant sections of NDS
6.2. Discrete inclusions, collages and co-cycles
6.3. Attractors of skew-product systems,collages and co-cycles
6.4. Chaotic attractors of discrete control systems
6.5. General case
6.6. Some applications
6.7. Global attractors of switched systems with continuous time

Chapter 7. Asymptotic Stability of Switched Systems pp.209-238
7.1. Switched dynamical systems
7.2. Asymptotic stability of switched systems with continuous time
7.3. Some test of asymptotic stability
7.4. Asymptotic stability of homogeneous switched systems
7.5. Slow homogeneous switched systems
7.6. Asymptotic stability of linear switched systems
7.7. Asymptotic stability of gradient switched systems
7.8. Asymptotic stability of discrete nonlinear switched systems
7.9. Homogeneous switched systems with discrete time
7.10. Asymptotic stability of discrete gradient switched systems

References pp.239-264

Index pp.265-269

   Series:
      Mathematics Research Developments
   Binding: Hardcover
   Pub. Date: 2010
   Pages: 269.pp
   ISBN: 978-1-61668-021-3
   Status: AV
  
Status Code Description
AN Announcing
FM Formatting
PP Page Proofs
FP Final Production
EP Editorial Production
PR At Prepress
AP At Press
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Global Attractors of Set-Valued Dynamical and Control Systems