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This book provides a broad introduction to the subject of dynamical
systems, suitable for a one- or two-semester graduate course. In
the first chapter, the authors introduce over a dozen examples, and
then use these examples throughout the book to motivate and clarify
the development of the theory. Topics include topological dynamics,
symbolic dynamics, ergodic theory, hyperbolic dynamics,
one-dimensional dynamics, complex dynamics, and measure-theoretic
entropy. The authors top off the presentation with some beautiful
and remarkable applications of dynamical systems to such areas as
number theory, data storage, and Internet search engines. This book
grew out of lecture notes from the graduate dynamical systems
course at the University of Maryland, College Park, and reflects
not only the tastes of the authors, but also to some extent the
collective opinion of the Dynamics Group at the University of
Maryland, which includes experts in virtually every major area of
dynamical systems.
This volume presents a wide cross section of current research in
the theory of dynamical systems and contains articles by leading
researchers, including several Fields medalists, in a variety of
specialties. These are surveys, usually with new results included,
as well as research papers that are included because of their
potentially high impact. Major areas covered include hyperbolic
dynamics, elliptic dynamics, mechanics, geometry, ergodic theory,
group actions, rigidity, applications. The target audience includes
dynamicists, who will find new results in their own specialty as
well as surveys in others, and mathematicians from other
disciplines who look for a sample of current developments in
ergodic theory and dynamical systems.
This book provides a broad introduction to the subject of dynamical systems, suitable for a one or two-semester graduate course. In the first chapter, the authors introduce over a dozen examples, and then use these examples throughout the book to motivate and clarify the development of the theory. Topics include topological dynamics, symbolic dynamics, ergodic theory, hyperbolic dynamics, one-dimensional dynamics, complex dynamics, and measure-theoretic entropy. The authors top off the presentation with some beautiful and remarkable applications of dynamical systems to areas such as number theory, data storage, and internet search engines.
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