Beck J. Strong Uniformity and Large Dynamical Systems

World Scientific Publishing, 2018. — 453 p. — ISBN: 978-981-4740-74-6.It is the first book about a new aspect of Uniform distribution, called Strong Uniformity. Besides developing the theory of Strong Uniformity, the book also includes novel applications in the underdeveloped field of Large Dynamical Systems.
Readership: Researchers in dynamical systems and ergodic theory and statistical physics.From Uniform Distribution to the Time-Evolution of Large Off-Equilibrium Systems
Traditional Uniform Distribution and Weyl’s Criterion
Strong Uniformity
High-Dimensional Configuration Space of Large Systems and Unrealistic Time Scale
Dimension-Free Strong Uniformity on a Realistic Time Scale
Rapid Approach and Long-Term Stability of Square-Root Equilibrium
Non-ergodic Time-flow: Closed Orbit Spherical Systems
Closed Orbit Polar Systems
Snapshot Randomness (I): Poisson
Proofs of Theorems 4.2 and 4.3General Models
General Model: Unique Ergodicity via Typical Rotations
Asymptotic Time-Lapse Randomness
Short-Term Time-Lapse Randomness: Multiple Mixedupness (I)
Extensions of Theorem 4.2 beyond the Gaussian Case
Extensions of Theorem 4.2 to Nonlinear Curves on the PlaneMore Applications of Theorem 4.2
Snapshot Randomness (II): Central Limit Theorem
Snapshot Randomness (III) Case of Closed Orbits
Time-Lapse Randomness vs. Snapshot Randomness (I): A Fundamental Difference
Time-Lapse Randomness vs. Snapshot Randomness (II): A Fundamental Difference
CLT Time-Lapse Randomness: Upper Bound 246More Results about Randomness and Stability in Equilibrium
Simultaneous Square-Root Equilibrium Relative to Nice Sets (I)
Simultaneous Square-Root Equilibrium Relative to Nice Sets (II)
Simultaneous Square-Root Equilibrium Relative to Nice Sets (III)
On the Square-Root Logarithmic Threshold in the Gaussian Case
Beyond the Applications of Theorem 4.2
The Case of Singular Underlying MeasureMore Proofs
Proof of Theorem 4.1
Starting the Proofs of Theorems 13.1–13.4
Completing the Proof of Lemma 27.2
Finishing the Proofs of Theorems 13.1–13.4
Starting the Proof of Theorem 14.1
Finishing the Proof of Theorem 14.1
Proof of Theorem 14.2
Multiple Mixedupness (II): Proof of Lemma 12.2True PDF