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A First Course in Dynamics

A First Course in Dynamics
with a Panorama of Recent Developments

  • Date Published: September 2003
  • availability: Available
  • format: Paperback
  • isbn: 9780521587501


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About the Authors
  • 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.

    • Authors are top experts in the area
    • Many exercises and examples, including computer exercises
    • Mathematically rigorous but with emphasis on a broad range of applications
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    Reviews & endorsements

    '… an excellent presentation of the modern theory of dynamical systems at the advanced undergraduate to intermediate graduate level written by two renowned experts in the field.' Zentralblatt für Mathematik

    'The book is written in a precise and very readable style, there are many useful remarks and figures throughout. It can be highly recommended to anybody who is interested in dynamical systems and who has a basic knowledge of calculus. The book is also an excellent introduction to the more advanced monograph written by the same authors.' European Mathematical Society Newsletter

    'I would recommend that all senior undergraduate physics and engineering students should familiarize themselves with its contents … it is a recommendation for a mathematical perspective on dynamics from an engineer for engineers - and from my discussions with practical physicists a similar recommendation from them.' Contemporary Physics

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    Product details

    • Date Published: September 2003
    • format: Paperback
    • isbn: 9780521587501
    • length: 436 pages
    • dimensions: 251 x 177 x 20 mm
    • weight: 0.758kg
    • contains: 140 b/w illus.
    • availability: Available
  • Table of Contents

    1. What is a dynamical system?
    Part I. Simple Behavior in Dynamical Systems:
    2. Systems with stable asymptotic behavior
    3. Linear maps and linear differential equations
    Part II. Complicated Behavior in Dynamical Systems:
    4. Quasiperiodicity and uniform distribution on the circle
    5. Quasiperiodicity and uniform distribution in higher dimension
    6. Conservative systems
    7. Simple systems with complicated orbit structure
    8. Entropy and chaos
    9. Simple dynamics as a tool
    Part III. Panorama of Dynamical Systems:
    10. Hyperbolic dynamics
    11. Quadratic maps
    12. Homoclinic tangles
    13. Strange attractors
    14. Diophantine approximation and applications of dynamics to number theory
    15. Variational methods, twist maps, and closed geodesics

  • Instructors have used or reviewed this title for the following courses

    • Dynamical Systems in Economics
  • Authors

    Boris Hasselblatt, Tufts University, Massachusetts

    Anatole Katok, Pennsylvania State University

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