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The study of attractors of dynamical systems occupies an important
position in the modern qualitative theory of differential
equations. This engaging volume presents an authoritative overview
of both autonomous and non-autonomous dynamical systems, including
the global compact attractor. From an in-depth introduction to the
different types of dissipativity and attraction, the book takes a
comprehensive look at the connections between them, and critically
discusses applications of general results to different classes of
differential equations.The new Chapters 15-17 added to this edition
include some results concerning Control Dynamical Systems - the
global attractors, asymptotic stability of switched systems,
absolute asymptotic stability of differential/difference equations
and inclusions - published in the works of author in recent years.
This book emphasizes those topological methods (of dynamical
systems) and theories that are useful in the study of different
classes of nonautonomous evolutionary equations. The content is
developed over six chapters, providing a thorough introduction to
the techniques used in the Chapters III-VI described by Chapter
I-II. The author gives a systematic treatment of the basic
mathematical theory and constructive methods for Nonautonomous
Dynamics. They show how these diverse topics are connected to other
important parts of mathematics, including Topology, Functional
Analysis and Qualitative Theory of Differential/Difference
Equations. Throughout the book a nice balance is maintained between
rigorous mathematics and applications (ordinary
differential/difference equations, functional differential
equations and partial difference equations). The primary readership
includes graduate and PhD students and researchers in in the field
of dynamical systems and their applications (control theory,
economic dynamics, mathematical theory of climate, population
dynamics, oscillation theory etc).
This book emphasizes those topological methods (of dynamical
systems) and theories that are useful in the study of different
classes of nonautonomous evolutionary equations. The content is
developed over six chapters, providing a thorough introduction to
the techniques used in the Chapters III-VI described by Chapter
I-II. The author gives a systematic treatment of the basic
mathematical theory and constructive methods for Nonautonomous
Dynamics. They show how these diverse topics are connected to other
important parts of mathematics, including Topology, Functional
Analysis and Qualitative Theory of Differential/Difference
Equations. Throughout the book a nice balance is maintained between
rigorous mathematics and applications (ordinary
differential/difference equations, functional differential
equations and partial difference equations). The primary readership
includes graduate and PhD students and researchers in in the field
of dynamical systems and their applications (control theory,
economic dynamics, mathematical theory of climate, population
dynamics, oscillation theory etc).
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.
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