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A First Course in Dynamics with a Panorama of Recent Developments

The theory of dynamical systems is a major mathematical discipline closely intertwined with all main areas of mathematics. It has greatly stimulated research in many sciences and given rise to the vast new area variously called applied dynamics, nonlinear science, or chaos theory. This introduction for senior undergraduate and beginning graduate students of mathematics, physics, and engineering combines mathematical rigor with copious examples of important applications. It covers the central topological and probabilistic notions in dynamics ranging from Newtonian mechanics to coding theory. Readers need not be familiar with manifolds or measure theory; the only prerequisite is a basic undergraduate analysis course. The authors begin by describing the wide array of scientific and mathematical questions that dynamics can address. They then use a progression of examples to present the concepts and tools for describing asymptotic behavior in dynamical systems, gradually increasing the level of complexity. The final chapters introduce modern developments and applications of dynamics. Subjects include contractions, logistic maps, equidistribution, symbolic dynamics, mechanics, hyperbolic dynamics, strange attractors, twist maps, and KAM-theory.

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Publisher
: Cambridge University Press.,
Collation
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Language
English
ISBN/ISSN
9780511998188
Classification
NONE
Content Type
text
Media Type
computer
Carrier Type
online resource
Edition
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Subject(s)
Mathematics, Differential and Integral Equations
Dynamical Systems and Control Theory
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Other Information
Cataloger
Arin
Source
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Validator
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Digital Object Identifier (DOI)
https://doi.org/10.1017/CBO9780511998188
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