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.
|Publisher:||Cambridge University Press|
|Product dimensions:||6.97(w) x 9.96(h) x 0.83(d)|
Table of Contents1. 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.