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A First Course in Dynamics

With a Panorama of Recent Developments

By: Boris Hassleblatt, Boris Hasselblatt, Anatole Katok

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Paperback | 4 September 2003

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436 Pages

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24.41 x 16.99 x 2.26

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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.

Industry Reviews

'... 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 fur 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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You Can Find This Book In

Non-Fiction Science Physics Classical Mathematics Dynamics & Statics Engineering & Technology Mechanical Engineering & Materials Materials Science Mechanics of Solids Dynamics & Vibration Mathematics Applied Mathematics

Nonlinear Science Technology in General Engineering in General Optimisation Linear Programming Probability & Statistics

What is a dynamical system?
Simple Behavior in Dynamical Systems
Systems with stable asymptotic behavior
Linear maps and linear differential equations
Complicated Behavior in Dynamical Systems
Quasiperiodicity and uniform distribution on the circle
Quasiperiodicity and uniform distribution in higher dimension
Conservative systems
Simple systems with complicated orbit structure
Entropy and chaos
Simple dynamics as a tool
Panorama of Dynamical Systems
Hyperbolic dynamics
Quadratic maps
Homoclinic tangles
Strange attractors
Diophantine approximation and applications of dynamics to number theory
Variational methods, twist maps, and closed geodesics
Appendix
Solutions
Table of Contents provided by Publisher. All Rights Reserved.

A First Course in Dynamics

With a Panorama of Recent Developments

At a Glance

Paperback

Industry Reviews

Shipping

How to return your order

Defective items

You Can Find This Book In

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