Strong Uniformity and Large Dynamical Systems (ePub)

-->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. -->Contents: From Uniform Distribution to the Time-Evolution of Large Off-Equilibrium Systems:Traditional Uniform Distribution and Weyl's CriterionStrong UniformityHigh-Dimensional Configuration Space of Large Systems and Unrealistic Time ScaleDimension-Free Strong Uniformity on a Realistic Time ScaleRapid Approach and Long-Term Stability of Square-Root EquilibriumNon-ergodic Time-flow: Closed Orbit Spherical Systems Closed Orbit Polar SystemsSnapshot Randomness (I): PoissonProofs of Theorems 4.2 and 4.3General Models:General Model: Unique Ergodicity via Typical RotationsAsymptotic Time-Lapse RandomnessShort-Term Time-Lapse Randomness: Multiple Mixedupness (I)Extensions of Theorem 4.2 beyond the Gaussian CaseExtensions of Theorem 4.2 to Nonlinear Curves on the PlaneMore Applications of Theorem 4.2:Snapshot Randomness (II): Central Limit TheoremSnapshot Randomness (III) Case of Closed OrbitsTime-Lapse Randomness vs Snapshot Randomness (I): A Fundamental DifferenceTime-Lapse Randomness vs Snapshot Randomness (II): A Fundamental DifferenceCLT Time-Lapse Randomness: Upper BoundMore 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 CaseBeyond the Applications of Theorem 4.2The Case of Singular Underlying MeasureMore Proofs:Proof of Theorem 4.1Starting the Proofs of Theorems 13.1–13.4Completing the Proof of Lemma 27.2Finishing the Proofs of Theorems 13.1–13.4Starting the Proof of Theorem 14.1Finishing the Proof of Theorem 14.1Proof of Theorem 14.2Multiple Mixedupness (II): Proof of Lemma 12.2Multiple Mixedupness (III): Proof of Theorem 12.2 --> -->Readership: Researchers in dynamical systems and ergodic theory and statistical physics. -->Key Features:It is the first book about the subject, so it is uniqueThe book is basically my contribution to the field