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Introduction To Nonautonomous Dynamical Systems And Their Attractors, An (Hardcover)
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Introduction To Nonautonomous Dynamical Systems And Their Attractors, An (Hardcover)
Series: Interdisciplinary Mathematical Sciences, 21
Expected to ship within 10 - 15 working days
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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.
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