Discrete Dynamical Systems with an Introduction to Discrete Optimization Problems
Publisher: Bookboon
Published: 2013
ISBN-13: 9788740303278
Table of contents: title: Part 1 One-dimensional maps; title: Preliminaries and definitions; title: One-parameter family of maps; title: Fixed points and periodic points of the quadratic map; title: Stability; title: Bifurcations; title: The flip bifurcation sequence; title: Period 3 implies chaos. Sarkovskii’s theorem; title: The Schwarzian derivative; title: Symbolic dynamics I; title: Symbolic dynamics II; title: Chaos; title: Superstable orbits and a summary of the dynamics of the quadratic map; title: Part II n-dimensional maps; title: Higher order difference equations; title: Systems of linear difference equations. Linear maps from Rn to Rn; title: The Leslie matrix; title: Fixed points and stability of nonlinear systems; title: The Hopf bifurcation; title: Symbolic dynamics III (The Horseshoe map); title: The center manifold theorem; title: Beyond the Hopf bifurcation, possible routes to chaos; title: Difference-Delay equations; title: Part III Discrete Time Optimization Problems; title: The fundamental equation of discrete dynamic programming; title: The maximum principle (Discrete version); title: Infinite horizon problems; title: Discrete stochastic optimization problems; title: Appendix (Parameter Estimation); title: References