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A First Course in Dynamics

A First Course in Dynamics
with a Panorama of Recent Developments

$69.99 (X)

textbook
  • Date Published: June 2003
  • availability: Available
  • format: Paperback
  • isbn: 9780521587501

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About the Authors
  • The theory of dynamical systems has given rise to the vast new area variously called applied dynamics, nonlinear science, or chaos theory. This introductory text covers the central topological and probabilistic notions in dynamics ranging from Newtonian mechanics to coding theory. The only prerequisite is a basic undergraduate analysis course. The authors use a progression of examples to present the concepts and tools for describing asymptotic behavior in dynamical systems, gradually increasing the level of complexity. 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

    "I highly recommend this book for an advanced undergraduate course in dynamical systems." Mathematical Reviews

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    Product details

    • Date Published: June 2003
    • format: Paperback
    • isbn: 9780521587501
    • length: 436 pages
    • dimensions: 251 x 177 x 20 mm
    • weight: 0.75kg
    • 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
    Appendix
    Solutions.

  • 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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