Discrete Dynamical Systems with an Introduction to Discrete Optimization Problems
Publisher: Bookboon.com
Published: 2013
ISBN-13: 9788740303278
Table of contents: title: Content; title: 1. Part 1 One-dimensional maps; title: 1.1. Preliminaries and definitions; title: 1.2. One-parameter family of maps; title: 1.3. Fixed points and periodic points of the quadratic map; title: 1.4. Stability; title: 1.5. Bifurcations; title: 1.6. The flip bifurcation sequence; title: 1.7. Period 3 implies chaos. Sarkovskii’s theorem; title: 1.8. The Schwarzian derivative; title: 1.9. Symbolic dynamics I; title: 1.10. Symbolic dynamics II; title: 1.11. Chaos; title: 1.12. Superstable orbits and a summary of the dynamics of the quadratic map; title: 2. Part II n-dimensional maps; title: 2.1. Higher order difference equations; title: 2.2. Systems of linear difference equations. Linear maps from Rn to Rn; title: 2.3. The Leslie matrix; title: 2.4. Fixed points and stability of nonlinear systems; title: 2.5. The Hopf bifurcation; title: 2.6. Symbolic dynamics III (The Horseshoe map); title: 2.7. The center manifold theorem; title: 2.8. Beyond the Hopf bifurcation, possible routes to chaos; title: 2.9. Difference-Delay equations; title: 3. Part III Discrete Time Optimization Problems; title: 3.1. The fundamental equation of discrete dynamic programming; title: 3.2. The maximum principle (Discrete version); title: 3.3. Infinite horizon problems; title: 3.4. Discrete stochastic optimization problems; title: 4. Appendix (Parameter Estimation); title: 5. References