Synopses & Reviews
Celebrated mathematician Shlomo Sternberg, a pioneer in the field of dynamical systems, created this modern one-semester introduction to the subject for his classes at Harvard University. Its wide-ranging treatment covers one-dimensional dynamics, differential equations, random walks, iterated function systems, symbolic dynamics, and Markov chains. Supplementary materials offer a variety of online components, including PowerPoint lecture slides for professors and MATLAB exercises.
"Even though there are many dynamical systems books on the market, this book is bound to become a classic. The theory is explained with attractive stories illustrating the theory of dynamical systems, such as the Newton method, the Feigenbaum renormalization picture, fractal geometry, the Perron-Frobenius mechanism, and Google PageRank." Oliver Knill, PhD, Preceptor of Mathematics, Harvard University.
Synopsis
Dynamic systems involve the mathematical expression of any fixed rule describing the time dependence of a point's position in space. Examples include mathematical models of the swinging of a clock's pendulum and the flow of water in a pipe. Celebrated mathematician Shlomo Sternberg of Harvard University created this book and supplementary materials for his course of the same name.It offers a variety of online components including PowerPoint lecture slides and MATLAB exercises.
Synopsis
A pioneer in the field of dynamical systems created this modern one-semester introduction to the subject for his classes at Harvard University. Its wide-ranging treatment covers one-dimensional dynamics, differential equations, random walks, iterated function systems, symbolic dynamics, and Markov chains. Supplementary materials offer a variety of online components, including PowerPoint lecture slides and MATLAB exercises. 2010 edition.
Synopsis
A pioneer in the field of dynamical systems discusses one-dimensional dynamics, differential equations, random walks, iterated function systems, symbolic dynamics, and Markov chains. Supplementary materials include PowerPoint slides and MATLAB exercises. 2010 edition.
Table of Contents
1. Iteration and fixed points2. Bifurcations3. Sarkovsky's theorem, Singer's theorem, intermittency4. Conjugacy5. Space and time averages6. The contraction fixed point theorem7. The Hausdorff metric and Hutchinson's theorem8. Hyperbolicity9. The Perron-Frobenius theorem10. Some topics in ordinary differential equations11. Lotka-Volterra12. Symbolic dynamicsBibliographyIndex