This book provides the first self-contained comprehensive
exposition of the theory of dynamical systems as a core
mathematical discipline closely intertwined with most of the main
areas of mathematics. The authors introduce and rigorously develop
the theory while providing researchers interested in applications
with fundamental tools and paradigms. The book begins with a
discussion of several elementary but fundamental examples. These
are used to formulate a program for the general study of asymptotic
properties and to introduce the principal theoretical concepts and
methods. The main theme of the second part of the book is the
interplay between local analysis near individual orbits and the
global complexity of the orbits structure. The third and fourth
parts develop in depth the theories of low-dimensional dynamical
systems and hyperbolic dynamical systems. The book is aimed at
students and researchers in mathematics at all levels from advanced
undergraduate up. Scientists and engineers working in applied
dynamics, nonlinear science, and chaos will also find many fresh
insights in this concrete and clear presentation. It contains more
than four hundred systematic exercises.
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