Estimating Physical Invariant Measures
and Space Averages of Dynamical Systems Indicators


Part I: Lyapunov Exponents

Chapter 1: Estimation of Lyapunov Exponents of Dynamical Systems using a Spatial Average

1.1 Lyapunov Exponents of Deterministic Dynamical Systems
1.2: Practical Estimation of Lyapunov Exponents
1.3: Lyapunov Exponents of Random Dynamical Systems
1.4: The Relationship between the Lyapunov Exponents of the Random and Deterministic Systems
1.5: Examples and Results
1.6: Discussion

Part II: Invariant Measures

Chapter 2: Computing Invariant Measures via Small Random Perturbations

2.1: Introduction
2.2: The Procedure
2.3: Increasing the Accuracy of the Approximation
2.4: Examples
2.5: Does Any Small Random Perturbation Work?
2.6: Discussion

Chapter 3: Finite Approximation of Sinai-Bowen-Ruelle Measures for Anosov Systems in Two Dimensions

3.1: Introduction
3.2: Equilibrium States
3.3: Approximation of the Weight Function
3.4: Computing the Approximate Equilibrium State
3.5: Discussion

Chapter 4: Approximating Physical Invariant Measures of Mixing Dynamical Systems in Higher Dimensions

4.1: Introduction
4.2: Outline of Method
4.3: L^1 and Strong Convergence
4.4: Sensitivity of Finite Markov Chains
4.5: Factors influencing the norm of the Fundamental Matrix
4.6: The Behaviour of Mixing Constants for Two Classes of Maps, and Numerical Results
4.7: Discussion

Chapter 5: Mixing Properties and Aggregation

5.1: Classes of Mixing
5.2: Estimating the Rate of Mixing of Perturbed Systems
5.3: Projected Perron-Frobenius Operators
5.4: Aggregation
5.5: Discussion