Intro
Preface
Acknowledgements
Contents
List of Figures
List of Tables
1 Introduction
1.1 Initial Concepts
1.2 Summary
2 One-Dimensional Mappings
2.1 Introduction
2.2 The Concept of Stability
2.2.1 Asymptotically Stable Fixed Point
2.2.2 Neutral Stability
2.2.3 Unstable Fixed Point
2.3 Fixed Points to the Logistic Map
2.4 Bifurcations
2.4.1 Transcritical Bifurcation
2.4.2 Period Doubling Bifurcation
2.4.3 Tangent Bifurcation
2.5 Summary
2.6 Exercises
3 Some Dynamical Properties for the Logistic Map

5.1 Linear Mappings
5.2 Nonlinear Mappings
5.3 Applications of Two Dimensional Mappings
5.3.1 Hénon Map
5.3.2 Lyapunov Exponents
5.3.3 Ikeda Map
5.4 Summary
5.5 Exercises
6 A Fermi Accelerator Model
6.1 Fermi-Ulam Model
6.1.1 Jacobian Matrix for the Indirect Collisions
6.1.2 Jacobian Matrix for the Direct Collisions
6.1.3 Fixed Points
6.1.4 Phase Space
6.1.5 Phase Space Measure Preservation
6.2 A Simplified Version of the Fermi-Ulam Model
6.3 Scaling Properties for the Chaotic Sea
6.4 Localization of the First Invariant Spanning Curve