Strong uniformity and large dynamical systems

Includes index

Includes bibliography (p. 437-438) and references

ch. 1 From Uniform Distribution to the Time-Evolution of Large Off-Equilibrium Systems 1.Traditional Uniform Distribution and Weyl's Criterion 2.Strong Uniformity 3.High-Dimensional Configuration Space of Large Systems and Unrealistic Time Scale 4.Dimension-Free Strong Uniformity on a Realistic Time Scale 5.Rapid Approach and Long-Term Stability of Square-Root Equilibrium 6.Non-ergodic Time-flow: Closed Orbit Spherical Systems 7.Closed Orbit Polar Systems 8.Snapshot Randomness (I): Poisson 9.Proofs of Theorems 4.2 and 4.3 ch. 2 General Models 10.General Model: Unique Ergodicity via Typical Rotations 11.Asymptotic Time-Lapse Randomness 12.Short-Term Time-Lapse Randomness: Multiple Mixedupness (I) 13.Extensions of Theorem 4.2 beyond the Gaussian Case 14.Extensions of Theorem 4.2 to Nonlinear Curves on the Plane ch. 3 More Applications of Theorem 4.2 Contents note continued: 15.Snapshot Randomness (II): Central Limit Theorem 16.Snapshot Randomness (III) Case of Closed Orbits 17.Time-Lapse Randomness vs. Snapshot Randomness (I): A Fundamental Difference 18.Time-Lapse Randomness vs. Snapshot Randomness (II): A Fundamental Difference 19.CLT Time-Lapse Randomness: Upper Bound ch. 4 More Results about Randomness and Stability in Equilibrium 20.Simultaneous Square-Root Equilibrium Relative to Nice Sets (I) 21.Simultaneous Square-Root Equilibrium Relative to Nice Sets (II) 22.Simultaneous Square-Root Equilibrium Relative to Nice Sets (III) 23.On the Square-Root Logarithmic Threshold in the Gaussian Case 24.Beyond the Applications of Theorem 4.2 25.The Case of Singular Underlying Measure ch. 5 More Proofs 26.Proof of Theorem 4.1 27.Starting the Proofs of Theorems 13.113.4 28.Completing the Proof of Lemma 27.2 29.Finishing the Proofs of Theorems 13.1Contents note continued: 30.Starting the Proof of Theorem 14.1 31.Finishing the Proof of Theorem 14.1 32.Proof of Theorem 14.2 33.Multiple Mixedupness (II): Proof of Lemma 12.2 34.Multiple Mixedupness (III): Proof of Theorem 12.2.