1 Posing the Problems
1.1 Initial Concepts
1.2 Summary
2 A Hamiltonian and a Mapping
2.1 The Mapping
2.2 Specific Applications
2.2.1 Standard Mapping
2.2.2 The Fermi-Ulam Model
2.2.3 The Bouncer Model
2.2.4 A Hybrid Fermi-Ulam Bouncer Model
2.2.5 Family of Mappings
2.3 Summary
3 A Phenomenological Description for Chaotic Diffusion
3.1 Dynamical Properties for the Chaotic Sea: A Phenomenological Description
3.2 Summary
4 A Semi-phenomenological Description for Chaotic Diffusion
4.1 A Semi-phenomenological Approach
4.2 Summary
5 A Solution of the Diffusion Equation
5.1 A Solution of the Diffusion Equation
5.2 Summary
6 Characterization of a Continuous Phase Transition in an Area-Preserving Map
6.1 Evidence of a Phase Transition
6.2 Break of Symmetry
6.3 Order Parameter
6.4 Topological Defects
6.5 Elementary Excitations
6.6 Summary
7 Scaling Invariance for Chaotic Diffusion in a Dissipative Standard Mapping
7.1 A Dissipative Standard Mapping
7.2 Analytical Description of the Diffusion
7.3 Summary
8 Characterization of a Transition from Limited to Unlimited Diffusion
8.1 Pieces of Evidence of a Phase Transition
8.2 Break of Symmetry
8.3 Order Parameter
8.4 Topological Defects
8.5 Elementary Excitations
8.6 Summary
9 Billiards with Moving Boundary
9.1 A Billiard Dynamical System
9.2 Unlimited Diffusion of the Velocity for the Oval Billiard
9.3 Summary
10 Suppression of Fermi Acceleration in Oval Billiard
10.1 Dissipation in a Billiard
10.1.1 Long-Stand Dynamics
10.1.2 Time-Dependent Regime
10.1.3 Discussion of the Phenomenological Results
10.1.4 Time Average
10.1.5 Determination of the Critical Exponents
