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Strong Uniformity and Large Dynamical Systems

Strong Uniformity and Large Dynamical Systems


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About the Book

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 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 4.3 General 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 Plane More 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 More 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 Measure More 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 12.2 Multiple 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 unique The book is basically my contribution to the field


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Product Details
  • ISBN-13: 9789814740760
  • Publisher: World Scientific Publishing Company
  • Publisher Imprint: World Scientific Publishing Company
  • Language: English
  • ISBN-10: 9814740764
  • Publisher Date: 07 Jul 2017
  • Binding: Digital (delivered electronically)


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